For a game you want to be so dependent on story, you have an issue here: huge cliches. This story could be done well if you do it right, but you'll have to be very careful with taking inspiration from other sources so it doesn't end up sounding totally contrived and cheesy.
Some ideas as to how to make it a bit better:
1. Focus more on your characters and less on the political and socioeconomic situations that contributed to the world's destruction.
2. Give them some vulnerability; no one likes perfect characters except their author.
3. Avoid the cliche of the scientists being overly analytical and having a lack of humanity.
Don't worry about it if you can't figure out where to take the story at first. Give it some time, keep it on the shelf, and work on some other projects.