2 categories sounds like a much-much easier solution... but your "sites" would be example.com/games and example.com/gear
You could probably set up pointers to display those pages via the subdomain URLs that you mentioned
Doing what you want to do (except for the subdomains), is built in to a single install of default WP. There's no need for multiple installs to accomplish just this.
It's fairly easy to make a Custom Category Template and different sidebars for each. Just read about custom templates in the Codex. By default your homepage will continue to show all the posts from both cats unless you change this.
However, if you did want to have multiple separate sites, you can do multiple installs now in a more elegant way called Virtual Multiblog (so you just have 1 copy of WP to maintain). There are other options similar but different from VMB.
I see this is from a couple months ago so now I wonder how you've worked it out!