OK, apologies for the silly question, and I'm sure there's going to be an answer that's going to leave me red faced, but.....

Uploaded our game, and you can find it when you search for "Horizon", but if you search for "Twine", it's not listed.  It's a free game, I'm "pretty sure" that all of the options that allow it to be searchable are ok. 

What have I done wrong?  Or have I misunderstood how the tags work?

Oh wow, that's a nice looking game. :) And it does show up in the 5th position if you click on "recently added". It must have slipped far down the list already in the popularity top.

OK, I was being an idiot!   Sorted now.  I thought the main search bar at the top would search tags too, didn't realise how the tag search worked.  Apologies, but thank you for the reply!  Gratefully appreciated.  And thanks for the nice comment about the game too.  I don't know if Twine games do particularly well in terms of popularity, but it's there for free for anyone to give it a go.

If you search for a name of a tag then the results will show tags that match on top, and you can click the tag to go into those games. Searching is generally for finding projects by title/description/author. If you want to browse then you'll have to explore through https://itch.io/games

Thank you leafo!  Still getting the hang of it!

Shouldn't the search really work by tags too? Most people probably take one look at the huge tag cloud and then go back to entering tags into the search bar.  (The page also says Top Tags, heavily implying not all are present, and should be looked through the search instead.)