Marking at least the games you already have in your library would be a cool feature. Made a script for that (can be used for more things). /t/1018893/a-never-show-me-this-again-please-button
Genres are tags for all intents and purposes. Except when you look at the url. The are written genre-xyz instead of tag-xyz. A game selects 1 main genre and up to 10 tags. And from this 10 tags you can select other genres as well. There is this browse box to enter tags ("select a tag"). All the genres are in that tag box.
You can filter games by language, but the buttons are hidden and you depend on developers to actually fill out that meta data. (I do not know if there is a listing of the languages, like /directory . I just hit this up from any game with the language attribute /games/lang-en )
Search itself was overhauled a short while ago. Maybe they overhaul browse next. The browse "search" is different from the actual search. There is a search that searches by title. And then there is the combination of filters, like tags and meta data - which some people also call search.