Is this version included?

I'm pretty sure there is no official Linux build of the original freeware Spelunky; there definitely isn't for the commercial remake.

Oh ok thanks. I was asking because I found many Linux Spelunky binaries in itch.io
thanks

The freeware game is open-source (non-commercial license). So any Linux builds of the original version may not be official, but as long as they're not being charged for, they should be fine.
For the record, the only two actual Spelunky-based game projects I see in itch's games section are a free, multiplatform (Windows + Linux + Android) reimplementation of the game in GameMaker Studio (ported from a much older predecessor), and a PWYW fan expansion mod for Windows & Linux that adds multiplayer and other stuff. (I guess the penguin version of the latter either requires or includes a community-compiled version of the game.)