I don't think just any old space game would fit the theme of "outdoors". However, there are many ways you could make it work. For example, spacewalks are very much outdoors. Anything where you (or units you control) go through a door (or something symbolic of a door) leaving a safe place to venture out into a strange and dangerous world would definitely qualify in my book. Get creative with it.
As for the advertising: it's pretty standard to include a link to your website in the end credits of your entry. Advertising a specific game would be a bit tacky though.