The answer is Yes you can cobble together a "PC" and run a bunch of old games using an emulator and not just DOS but Apple, Commodore, Amiga, etc... MAME... I have done this on a RasPi and any Linux machine. What you will find is problems with doing so legally and finding all the software (which is going to be pirated and cracked). You may also have trouble getting gamepads and joysticks working out of the box but it can be done. People make RasPicades all the time with thousands of games.
Maybe these guys are getting licenses for everything but I have a hard time believing they can do so and still make a profit at $99? I do not think they are using a RasPi solution. The hardware costs, enclosure, peripherals, power supply at their scale of market and all the assembly will cost too much. If they want to keep costs down they will make a custom closed emulator with preloaded games that cannot be changed running on some custom chip meant for this stuff, all loaded in the ROM... Like those "50 game in one" boxes you plug into your TV and play without any idea of what is inside or ability to change. They may be using something like that but got the manufacturer to customize the boot menu and screen and case to give the "effect" it is a little PC for nostalgic marketing purposes.
Until we see what is inside this thing and how much the user can customize or add their own games, there is no way to know. But like I said, $99 for an actual real little PC running actual licensed games (30 of them) and the ability to load in whatever you may have as legacy DOS software (I presume from some SD card) doesn't seem to leave them much profit. Does this thing have internal storage? Does it run off an SD card? Does the board even need Ethernet? Wifi? Chances are not... You could strip down some cost by removing certain features, and lower the RAM. Would you run Windows on it? RasPi would be overkill for their purpose if they want to keep costs down. As far as adding new games, if there is internal ROM pre-built with the games they will be getting in the basic system, they may offer an SD card to insert (like a little floppy disk) with add-on software that would more games to be added in the future. I don't think the target user for this device is going to be fussing around with installing and modifying SD card contents... It sounds like they are making it as easy as possible for someone to buy, plug and play, and choose from a menu... And added games will come as extra SD cards already pre-configured. I don't think you will be able to play around too much with your own stuff, nor would you want to. If you did then you'd already be using DOSbox on your PC. I don't think they are marketing to the hacker crowd, but to a nostalgic gamer (40-50 year olds) who want to remember their youth.