A Commodore 64 or TI-994A could. Probably not at 60fps, but it could be done. It would definitely need to be done in assembly, or with a modern compilation tool, like cc65.
The sprites would have to be hardcoded, instead of being interpreted from images. You would also have to be extra smart about what you're calculating/rendering, but keep in mind that your screen is probably only 40 characters wide, so the amount to render is exponentially smaller.
You'd be amazed what can be done on those older computers when the developer understands how the processors work on the ground level.
At the very least it'd be an impressive tech demo for something like the Commander X16[0], a new 6502 based computer running at 8mhz.