In my experience, games as simple as Breakout and Pong are laggy on my Apple watch and they are written natively to WatchOS so I think your, "more capable of running them", comment is a highly optimistic. I think the emulation software would bring to run NES, Atari, etc would bring it to it's knees much like this Win95 demo did.
The Apple Watch's S1 has a 520MHz 32-bit CPU with 32KB L1 cache, 256KB L2 cache, 512MB RAM, a PowerVR SGX543 GPU (same GPU as the iPhone 4s or PS Vita with one core instead of two/four and a lower clock rate) with shared VRAM, and needs to push enough pixels to fill a 312×390 screen on the larger model.
The NES has a 1.8MHz 8-bit CPU with 2KB RAM and maybe a 1KB more in a cartridge and a 2D GPU with an effective 284 bytes of L1 cache and 2KB VRAM, which needs to push 256x240 pixels of screen, plus some possible coprocessors in cartridges.
The SNES has a 3.6MHz 16-bit CPU, 128KB RAM, 64K sound RAM, possibly some extra RAM in the cartridge, a 2D 3.6MHz 16-bit GPU, up to 32MB of rapidly accessible ROM data, and with outboard chips maybe a 21MHz 16-bit 3D GPU or a 10MHz CPU.
And that takes us through 1990. Even the PS1 only has a 34MHz 32-bit CPU, 2MB RAM, and a 3D GPU with 1MB VRAM capable of rendering way less polygons than the PowerVR SGX543.
Overhead of WatchOS itself (a very stripped down version of UNIX), or background tasks (networking, timekeeping, health input tracking, etc), or an inefficient method of drawing graphics, or inefficient game-specific APIs available to native apps, or any number of other reasons specific to software may and probably would prevent the S1 from actually running an emulated or native version of an NES or SNES game at full performance.
But in terms of the hardware itself--which is what I was talking about, since this is a purely hypothetical "look what computing can do now"--the Apple Watch is ridiculously more powerful than any game system available through the 16-bit and even the PS1/N64 era, so if your goal was to run every game made through 1990 on the hardware and you had the resources to program the thing at a low level, you most certainly could.
For that matter, if you were to be able to code a
native version of Windows 95 for it (rather than one running in software emulation), to replace WatchOS, I'm quite sure you could get it to run as well as it did on a computer from 1995. Actually, since Windows NT4 could run on multiple CPU architectures including RISC ones, it'd be a better target for a port in this hypothetical world where Microsoft wanted to dust off an ancient OS and port it to ARM.