We bought our sons (ages 7 and 4) a couple of those plug-and-play arcade games. Each has several retro games including Pac Man, Ms. Pac Man, Galaga, Pole Position, etc. They really enjoy them and it takes us waaaaaay back. It’s also holding them off on getting a gaming system which, thankfully, hasn’t been asked for (yet).
The plug-and-play systems vary a lot in terms of quality. Many simply use a famiclone chip, often refered to as "Nintendo on a chip" or NOAC. Those are basically equivalent to the Nintendo Entertainment System hardware, with code for whatever games they're doing. The original Flashback used a NOAC along with games that were programmed to kinda sorta look like the original Atari 2600 games.
Far more interesting is the Flashback 2. That uses a custom CMOS-based chip which was based on the original NMOS designs for the 2600 (the most amazing piece of gaming hardware ever!). If one wires in a cartridge port, it can even run the vast majority of games for the original 2600. Since the original NMOS designs used some tricks that are hard to mimic using modern CMOS technologies, the design doesn't perfectly match the original, but it's still neat to see such a classic design get a new life.
Actually, I think the 2600 is a beautiful illustration of the power of the microprocessor. Unlike most gaming systems, whose hardware is designed to display various objects on a frame of video, the Atari's hardware doesn't even have any concept of what a "frame" is. Such concepts are handled entirely in software. Although this makes programming the 2600 'interesting', it allows for a level of flexibility which is entirely unmatched by anything else of its era. I think it's neat that essentially the same design is being produced in the Flashback 2. Even though the design is 30 years old, there's probably more undiscovered territory there than on many other platforms.