How to submit a site there is no direct category for.

[neveremail]

LLs are generally for submitting freesites too only.

You may get a few LLs that accept your site but its not really worth it. What you should do instead is make freesites on your existing site and submit them to the LLs and on your freesites have a link back to your main games site, this is an ongoing thing where you will make a few freesites each week.

Or alternatively approach some LLs for a link exchange.