You speculate too much. Better to look around and see for yourself. The MasterPlay, Digital Joystick Adapter, etc. are digital joystick interfaces for the Atari 5200. They are not analog joysticks that you use with them nor are they called analog joystick interfaces. Human is thinking discrete motion and he interfaces with a digital joystick. It's not purely digital since the digital signals have to be converted to analog and back to digital and slow sampling rate, but still when I move right, I won't be producing a range of values from center to 228. Similarly for other directions. It makes a HUGE difference in the uncertainties that I talked about. And obviously, the throw is the same as digital joystick since it's the same joystick.
LOL, yeah after all my comments about purely digital joysticks with long throw and wide range (high precision) control, or even ones with long throw and only low precision (I believe the odyssey 2 is like that -long throw, spring centered, 9 state digital).
Let alone my comments about joystick implementation in general being a huge factor: ie functionality, form factor, reliability, etc. (general human interfacing issues not related to analog or digital control)
OK, then what was the point about using only the digital button lines on the PC that you mentioned earlier??? (other than polling speeds...)
And what about controllers only using 4 switches but with throw length and/or accuracy worse than the 5200? (and that's not just hypothetical, but applicable to many real-world cases like the Oddyssey 2, Intellivision or various poorer quality or just oddly designed joysticks/gamepads be it 3rd party or 1st party) Of course the same range of issues applies to analog (or digital) high precision controllers.
That IS all analog though and to call it "digital" is a misnomer generated by pop culture: it's like calling Asteroids or Atari Star Wars (or ESB) in the arcade "video games" ... they're electronic games, but not video in the slightest. (pure CRT vector displays, no video -ie raster- scanning at all unless it's done in software -I think the vectrex may have a raster scan mode or does raster text in software for some displays) Or case in point: how the N64's thumbstick is called "analog" when it's fully digital as much as an optical track ball or ball mouse is. (or how programmers often consider all high-precision control "analog" regardless as they see it all as high precision digital data only and have no telling wither analog or digital mechanisms were used at the source input device)
Or the opposite, where you have throw distance and feel no different from a normal 4-switch stick/d-pad but replace the dome switches with pressure sensitive switches (like piezoelectric) that have high precision AND may even be truly analog (ie voltage based) in nature but may be used exactly like low precision on/off switches (from the user end -slightly different at the programmer's end) or allow the full analog precision to be used. (pressure sensitive control like the d-pad and buttons on the PS3)
All those interfaces ARE analog... and getting down to it there's nothing analog or digital about many other control mechanisms in real life. You could have a mechanical switch with 2 positions operating some function on a machine, but that's neither analog nor digital as it has nothing to do with electronics without further context.
You have some fully analog devices that have simple 2 state switches used too, but the system is still all analog in design.
A light switch is neither analog nor digital in that sense either unless it's specifically applied in the context of electronics... though it makes a good analogy for a 1-bit digital switch.
Another case would be a telegraph, a fully analog device though (normally) using a data pattern analogous to binary code. (it's not simple on/off though, but more like pulse density modulation or pulse width modulation)
A hydraulic/mechanical joystick/yolk in an aircraft is neither analog nor digital for that matter.
One thing that really blurs this is cases of analog to digital converters and digital to analog converters. Human motion/input is never analog or digital, but it will relate to analog or digital input/output depending on the device being used.
As such, all final inputs to such computers will be digital (if there's analog anywhere, it's converted to digital at some point), the question is if there's analog mechanisms in use, and what those mechanisms are. You could have full digital control where there's only switches being grounded, no variable voltage, no voltage supply at all (other than use for peripherals or serial data encoding), and direct parallel output (or encoding to serial or multiplexing), but then there's use of pots (with anywhere from virtually no throw to very long throw) or pressure sensitive material that starts analog and is converted to digital (but other mechanisms providing similar functionality with pure on/off digital electronic mechanisms), and finally you have low precision "digital" to analog to digital hacks as well.
The latter as such would technically be analog in nature either way, but you could look at it rather like a resistor DAC for audio taking digital bits and outputing analog voltage with the exception that it's a human interface device and the initial input is neither analog nor digital but a human input via touch (etc), so it's analogous to an ADC if the human was treated as a digital computer... but anyway this the mechanism often terms "digital" due to the 8-way 9-state like control provided (technically more states than that due to analog drift and such, but the Analog to digital process and software would sort that to 9 acceptable ranges just as with higher precision controls)
It's an analog controller with effectively a 2-bit precision output per axis (the ADC used in POKEY is 8-bit regardless, so sorting would be done at 8-bit resolution with acceptable error/drift/calibration taken into account).
You could have a controller with the resistors built in and directly connecting to the necessary lines and switches with minimal wiring/electronics (and would obviously be significantly cheaper than using potentiometers and not much different in cost from a plain switch based controller with parallel output) a normal switch based stick that was acting as a normal digital joystick internally, and in that case you would have more of an argument for a true digital to analog conversion taking place (except there's no digital sampling to convert to analog, just raw parallel switch connections/states) and you'd need a slightly more complex interface externally, or at least a bit more wiring, but basically the same thing.
For the VCS/A8 and other 2 axis types it would be different from the 4 axis vectrex mechanism (which would actually be a bit easier in some respect, but in all cases you'd only need some resistors and wiring. (and calibration pots if the system you were using didn't auto calibrate on a per controller basis)
I've seen some rather elaborate mechanisms used pointlessly (or seemingly so)... but all you should need is to take the normal 4 directional lines +gnd line and connect them such that "GND" pulls +5V and the converter "box" naturally outputs suitable resistance for neutral to both pot lines, the "low" positions (I assume left an down are used on the 5200) would connect directly to ground (overriding neutral), and up/right would connect to a low resistance values (preferably not bare 5V as some games have issues with that) that similarly override the neutral values. (and for the fire buttons, pull through the gnd used for dn/left) So you'd have one common neutral voltage constantly connected to the POT lines and have the pot inputs get shorted to gnd or higher voltage value for the up/dn/L/R states. (so the neutral voltage would get grounded or the higher voltage would be connected in parallel)
I seem to recall a simple schematic for such a controller on Atarimuseum.
For the vectrex it's a bit different: you'd have gnd set as neutral for all axes (a neat design avoiding centering calibration entirely, but requiring both + and -5V supplies) and suitably low resistance to provide the maximum upper range for each axis pulling though positive or negative voltage correspondingly -the vectrex uses +/-3.4V. (and the buttons pulled through gnd as normal)