I think we're ready to get past the "retro or modern" labelling, previous poster has tried to split it into categories, I think something a little more broad reaching and long lasting could be something like this:
Antique: Early pinball, redemption games, pre-WW2 arcade games etc. While not video games as such, and certainly not home systems they represent anything that is considerably rare and old enough to be a specialist purchase. You probably have to go to an expert to get these restored/repaired - or be a strong enthusiast yourself.
Vintage: Electromechanical arcade machines in the 60's and 70's, and anything that uses RF signal. My logic is this: As a child I knew about tuning in stations to get systems to work, it was just something I needed to do to get it to work, kids these days don't need this, they'd have to have "special" knowledge to get a system working. Vintage systems and machines is not the purchase of the casual user, if you are buying this kind of stuff, you want to keep / play it out of a genuine interest or collection building.
Retro: My logic for using this word is below. This is for the NES, Master System, Mega Drive, SNES, PS1 and the Turbografx - these have (or about to have) mini/classic versions which is intended as nostalgia. Most people who buy the original consoles too at this point do it for nostalgia (I've sold plenty of consoles to people who aren't collectors, but rather people around my age who wants to play the old games again in the way they remember). Although Saturn / N64 doesn't have classic versions, I think they still fit into this category.
Pre-Modern: I find it hard to label what PS2 and Dreamcast should be in, its a common problem I think so this category is for them.
Modern: Last gen and current gen, PS3 and 360 still have some services so I think they should be still counted in this.
My logic on the wording is this:
Antique: Usually left for things that is a 100 years old, its not always so strictly applied. Video games is not 100 years old yet, but early arcade and pinball machines are - and they exist as precursors to the home systems. On wikipedia it is described as: "is an item perceived as having value because of its aesthetic or historical significance" and " is usually an item that is collected or desirable because of its age, beauty, rarity, condition, utility, personal emotional connection, and/or other unique features. It is an object that represents a previous era or time period in human history."
Vintage: Immediately after wikipedia's definition of antique it has: "Vintage and collectible are used to describe items that are old, but do not meet the 100-year criteria.". The use of the word vintage for objects is relatively modern, and there is debate about how old something should be before it classifies. Most say at least 20 years, which would easily match the kind of consoles that I included. I think Vintage also helps to suggest that there is some degree of interest / knowledge that is now deemed specialised. Remember, we're all getting older!
Retro: The use of the word retro now has many uses, but in most other forms outside video games retro usually means a quite specific style, or use. I think we need to get out of the use of the word retro to mean a broad range of non-modern games as there is certainly a variety and history we can now explore. Retro in the designer / interior world tends to mean anything from 1950's to 1980's, but its more than that - its the idea of it being functional and chosen by design in a modern period. Take the guy in the UK who lives in the 1940s styled house and hosts school trips - he lives retro despite the fact he could clearly have a flatscreen tv, a microwave and wifi. He chooses not to. Similarly, nostalgia is flooding the market with mini/classic machines. This isn't particularly for the collector or enthusiast, we feel its too limited with "only" 20-40-60-100 games, but rather for the casual players or prior gamers who say things like "oh man do you remember sonic the hedgehog!!!".
Pre-Modern: Ahaha, I think this is pretty much the "whatever is left" category. I think I too struggled with the PS2 period, it was quite instrumental time for the gaming industry, not just the PS2 but the other consoles too. Dreamcast had functional internet use, PS2 had DVD playback, X Box had... whatever it had and Gamecube had loads of accessories. I think Wii probably fits here too now, as its services is now completely dead.
Modern: The average user has these, they double up as home entertainment machines. In fact, like mine, they are probably used MORE for watching TV than playing games. PS3 is a cheap blu ray player, X Box One's is for kids playing fortnite, which ever console you have, you or someone else in the house probably use YouTube or amazon or netflix on it.