Some ideas
I'm almost certainly going to have to give this one a miss, so here's my idea dump if you're struggling to think of anything!
Start with nothing / Mutation / Evolve to survive
Collect things, maybe body parts for a robot or an evolution game? You've got really low health and can't attack, but can build yourself up and fight back. Maybe even just a really basic top down shooter with an open level (+1 for proc gen, my code for random walker level gen in Unity is here), body parts do things like different attacks, more health, movement abilities - whatever you've got time for! No need for a save state, it's more fitting for the theme if you have to start again every time. This is actually really low scope, with the option of adding extra bits in based on how much time you've got left.
Unconventional travel
Pressing forward moves you backwards & vice versa? I don't know, really don't like this theme lol. It's boring and is too close to the usual "make a bad game" themes.
Side effects
"Powerups that hurt you" is going to be SO overdone, maybe a story-based text RPG? You have to make meaningful decisions, each one of which has a lasting effect. Maybe you choose to save someone, but at the cost of someone else's life. Or you go down one corridor, only to have the other one permanently blocked off.
Small character, big enemies
Shadow of the colossus, anyone? :joy: a few big boss battles, where each one has a really specific weak point. I think that could be really fun! I'd make it as a side-scrolling shooter because that would be the easiest for me personally to implement. No need for additional weapon types or anything like that, the challenge is in learning the boss attack patterns and avoiding them. You could also do it as a bullet hell game!
Factory
You're a factory worker working in QA - you've got to decide what's good and bad. Fast paced tinder - you could do it as a mobile game, maybe even do it to a beat so it becomes a little like a rhythm game? Bonus points for accepting/rejecting things to the beat. IDK, I don't like this theme and think it's just going to be a load of construction themed games, which I'm not a fan of. I guess you could do an FPS set in an industrial factory, that might be fun :joy: all I can think of is dark and grunge-y aesthetic, though, and I don't like that.
Shelter
A radiation-stricken world, you have to venture out of your shelter to collect food/resources etc - but stay out too long and you get radiation sickness, impacting your stats in some meaningful way. Too many rads and you die. Run out of food and you die.
One item, many uses
Wow, I actually don't have any reasonably scoped ideas for this. Sure I can think of something cool, but it would require a fully featured game which just isn't feasible in a weekend :joy:
Night is coming
See the shelter game, but swap out radiation for darkness and radiation sickness for insanity, and you're good to go :joy:
Making connections
Puzzle game like Bioshock's "hacking" minigame! Make connections between wires to fix things - maybe set it in an apple "genius" bar :joy:
Isolation
A typical top-down RPG, but when you get close to NPCs they move away. You can't buy or sell anything, you don't get given anything and you have to do everything alone. Because everyone hates you. Maybe throw in a plot twist where the main character snaps and slaughters the village :wink:
Duplication
Duplicate/destroy to reach new heights! Some sort of platformer along the lines of "thomas was alone", but instead of switching between colours, you duplicate yourself and destroy the duplicate to solve puzzles. Your duplicate moves with you.
Low Tech
Make any game you want, but do it in a fantasy setting. Seriously, what's the point of this theme?
Take one, leave the rest
See Start with nothing / Mutation / Evolve to survive, but make it level-based and at the end of every level you get to choose between a few body parts. That sort of thing is going to be overdone, but bleh that's what happens when the theme is incredibly mechanically limiting like this.