The 5200 is no slouch either. The 5200 is basically a slightly-tweaked Atari 800, and those machines had a separate almost-CPU called "ANTIC" that interprets data for the screen fetched via DMA based on a programmatic "display list". This independent unit then shoves the data into the "C/GTIA" chip which is an enhanced cousin of the TIA chip used in the Atari 2600, and itself has some rudimentary intelligence. (IE, it renders "Player/Missile" screen components, Atari's version of sprites.) Essentially the ANTIC works to offload some of what the main CPU had to do in the 2600 and allows the C/GTIA" to work with "real framebuffers" instead of the single-line buffer the *extraordinarily* RAM-constrained 2600 used.
(And the NES, likewise, has an independent "PPU" that includes its own onboard RAM and DMA engine and offloads a lot of work from the main CPU.)
There was a "semi-functional" Atari 800 emulator for the Atari ST (which is a substantially faster machine than the IIgs) but when running graphics modes it ran at less than 1/10th the speed of the real thing. (By comparison, an Apple II emulator by the same author for the ST could run at 40-50% of full speed, which indicates just how much overhead gets sucked up emulating elaborate graphics hardware.) You might argue that since a IIgs wouldn't have to emulate the main CPU it would have more left over for emulating the hardware, but... I'm skeptical one could easily write an emulator that could run an original unmodified binary "natively". You'd have to have some mechanism to "trap" attempts by the emulated binary to access hardware devices and interrupt program execution to run the hardware emulation code. On a simple machine without an MMU I just don't see it happening.
(The closest example I can think of is Shapeshifter/BasiliskII for the Amiga, which manages to run a MacOS emulation without true "virtualization", but it cheats *a lot* and falls down hard if presented with any non-well-behaved program that tries to tickle hardware without going through the MacOS ROM. Tickling hardware is *all* that 8-bit game programs do so it's really an apple-to-oranges comparison.)
Of course, the IIgs is easily fast enough to run a decent port of most 8 bit computer/early console games. Rewrite the graphics and sound routines to use the native hardware and you're good. (The IIgs has weaker video capabilities than most 8 bit game platforms as it lacks sprites, but its CPU is enough more powerful to compensate in most cases.)