I've been focusing on low-level programming for retro console games for the past few months, so I'd like to know if it's permitted for me to make a game in .rom format that only runs on old consoles or emulators.

OO that'd be fun. I don't see why you shouldn't be allowed to make a .rom! Just make sure that it's clearly labelled that it's in that format. I also think it should be ok to list whatever emulators it runs on? I'll leave that part up to your discretion, though. But, yeah! By all means, make a ROM that sounds cool as heck.