In particular, I like the part where you build your deck from a set of themed sub-decks before the start, and then it's up to you to find the synergies between those themes. Not sure if there's an existing term for that mechanic. I think it may count as a form of a deckbuilder, but editing the deck's contents isn't part of the main game loop. Maybe a deck drafter?
I also like that it's a compact card game that doesn't take long to learn or play, and plays well with only 2 players. The only other drafting games I've found have a board, lots of pieces, and are aimed at 4+ players.
Trying to search for games like Compile is a bit difficult, because in the other threads I find, people like to focus on the lane battling aspect, which I could take or leave. I'm mostly interested in compact drafting games for 2p. Anyone know any?
For lane battlers where you mix sub-decks my favorite is Riftforce, especially once you add the expansion to increase the number of available factions. The factions are drafted and each player ends up with 4 factions. Cards from a given faction share the same power but have different strengths. This gives a good variety of abilities but since there are only 8 in a given game they are still easy to keep track of and plan for.
Tyrants of the Underdark, is a bit different but I like it a lot: a river-market style deckbuilder where the market deck is a mix of two themed decks. The current edition comes with 6 factions.
If you are open to coop/solo then Marvel Champions is somewhere halfway into this direction. Each hero comes with a small preset deck and you then customize this by picking cards from exactly one of the four aspects (factions) available in the game.