Since games made for the XM unit cannot play on a 7800 by itself, saying that a game made for use on the 7800 with an XM unit is not a 7800 game is completely accurate.
Since the XM unit cannot play games by itself, saying that a game made for use on the 7800 with an XM unit is not a 7800 game is not accurate.
I'd like to disclose, up front, that I ordered a 7800XM within days of the order page being posted.
That said, I think it's worth exploring ZyloneBane's point, which I believe can be summarized thusly: if you can't pop a cartridge into a stock 7800 and play it, then it's not a 7800 game; it's something else.
Seems simple enough, but let's consider the 7800 game, Commando. That's a 7800 game that you can pop into a stock unit and start playing. However, I believe the cart has both a POKEY chip and some extra RAM onboard. So, the cartridge actually enhances the 7800's hardware to deliver a better gameplay experience.
I am interested in, someday, writing a 7800 game or two (in my copious spare time), and if I were to engage in such an undertaking, I am certain I would like to have additional RAM and a POKEY. In the late 1980s, I would have used a cartridge with hardware enhancements similar to Commando's. However, back then, I would have (hopefully) been able to sell more than 100 or so of them, so the cost of the enhanced cartridge could be absorbed.
These days, the tiny market for 7800 games mean the cartridges themselves have to be as close to free as possible. The 7800XM provides a way to accomplish that. It allows homebrew games to offer the same hardware that, historically, would have been found within the cartridge itself (and the YM chip is a bonus), but users only have to buy it once. If the hardware enhancements were still buried in the carts, users would end up paying over and over again for the extra RAM and POKEY chips. This way, they only have to buy the enhancements once.
So, going back to the premise that a game is a 7800 game only if it runs on a stock system, consider this:
If somebody hacks Commando to offer additional levels and then releases that as a new cart for the 7800XM, is that no longer a 7800 game? In that scenario, the code is pretty much the same, but there are more maps, and the POKEY and extra RAM are provided by the 7800XM instead of being embedded.
I can see it being argued either way, but in the end, I see the 7800XM as an enabler of high-quality homebrews for the 7800 - in an age where the economy of scale won't absorb carts with additional hardware onboard.