My ideas
At first, I didn't like the theme. But I started reading some of the posts here and thinking about all the different ways to interpret "Running out of space" and writing them down. Then I got some sleep. The ideas started to come gradually this morning, and now I've picked one that I think I will be able to make into a fun game.
Here's my list, feel free to steal my ideas!
Popular restaurant. You are the Maitre'd and you have to assign diner groups to tables.
Disk drive is getting full. You need to delete some files. But which are vital code? Replace drives in racks in a server farm.
Hospital beds
Orbital debris. You are a space janitor, and you have to clean up orbital debris for satellites and rocket launches. https://www.space.com/24895-space-junk-wild-clean-up-concepts.html
Car parking spaces
Big family in a small house. Clear out rooms or save for an extension.
Running = Smuggling. in space.
Literally running. Spacewalk race?
Running = Managing. Space delivery company?
Running = Creeping/growing tendrils from space
Personal space. You have to navigate a crowded street/tube/etc without maxing out your proximity meter or anyone elses - otherwise you/they lose it!
Outer space.
Inner space. Nano entities inside a body.
You are defending against enemies that consume the ground you are on. You need the ground around you for resources.
When you fail, the path you took is closed off.
You are getting bigger. You have to escape before you get stuck. Might work with Inner space.
I've already spotted some of these ideas in the feed - great minds think alike!