Are we restricted to the ASCII character set?  Or can we display arbitrary graphics as long as they're divided into 5x8 or 5x10 blocks?

I assume this is intended to run/simulate a HD44870 16x2 display.

However, a few different character sets exist for those. Example https://arduino.stackexchange.com/questions/46828/how-to-show-the-%C2%BA-charact...

And they allow up to 8 custom characters to be displayed at a time.

The purpose of the jam is to make a game whose display is similar to one of those displays.

You can use one of the character tables, as daid said, also with 8 custom characters. But you can do whatever you want, as long as they stay within the 5x8 or 5x10 character grid.

So, 16x2 "characters", each 5x8 or 5x10 pixels in size. And (at least) one empty pixel between the characters?

I read this now as: Just make it appear like the LCD, do not set yourself to the strict limits of this LCD. (Bit like shovel knight looks like a NES game, but doesn't do any of the actual limitations)