That's some wacky smooth animation for the Apple II. It's quite a feat to have multiple apparent sprites move so smoothly like that.
Apple II high resolution graphics are 280x192 pixels stored in 8 kilobytes at 2000 - 3fff or 4000 - 5fff. (With a fun interleaving where bits in memory are not in the same order as the bits on the display. Woz saved a few chips that way.)
That is to say, there are no hardware sprites.
The fastest way to clear the display is an unrolled loop in the form of LDA #0, STA $2000, STA $2001, STA $2002 etc. That works out to about 30,000 cycles which takes 30 milliseconds. A more plausible operation - displaying a whole-screen bitmap by copying it from another location in RAM to the framebuffer using a loop with indexes - weighs in at several hundred thousand cycles, or an appreciable fraction of a second.
This game achieves its smoothness by synchronizing to the video refresh. That's not a particularly challenging thing to do, but it wasn't a viable option for commercial games back in the day due to uncertainty of how to do it properly across the different Apple II models.
Apple added VBL polling with the IIe in 1983, and then broke it a year later with the IIc. And an unfortunate typo in the IIc technical reference manual meant that developers couldn't figure out how to do it properly.
The only official, cross-platform way to do it was through the mouse firmware, but most users didn't have the mouse hardware installed.
This game uses the mouse firmware, if available (II+ w/ mouse card, IIc, IIgs), to generate VBL interrupts. On the IIe without a mouse card, it polls for VBL.
By the way, if you're running this game on the Virtual ][ emulator for MacOS, be sure to disable the mouse card. Its emulated mouse card only generates VBL interrupts at 30 Hz, so the game runs at half speed.
My initial imposter syndrome came from not being able to understand enough machine language and the Apple II graphics format to be able to duplicate Ultima IV (with simultaneous sound and animation).
But this exists now: https://github.com/fadden/fdraw
Wild if Apple had had something like a library or framework with this kind of stuff in the Apple II days.
Not at all the same, but they did have QuickDraw II for the IIgs. This library had the benefit of using the simpler IIgs graphics modes, avoiding all the Apple II weirdness. With a little bit of searching the source can be found online.
I had an Apple][+ and can confirm that the HiRes mode was devilishly difficult to work with, to the extent that even many commercial games had visible artifacts and flickering.
These smoothly moving graphics over a background image would have blown everyone out of the water in 1982.
Now imagine working with the double hires mode with vertical interleaving that has already been discussed and horizontal interleaving between the main memory and bank switched memory to the higher 64K of extended RAM.
having VBLANK available works wonders, see this double-hires code I just put together that only looks nice due to the magic of VBLANK on Apple IIe/IIgs (Apple IIc is much harder to get VBLANK from if you're playing music with interrupts) https://www.youtube.com/watch?v=1QwUGFDcQcI