By amazing coincidence of timing, I am having this issue also. Installed the itch.io deb on my Debian 9 desktop, I can download the game, but it won't run. Are there troubleshooting resources for itch.io?
Edited to add: I did a bit of searching on the error message "reconfiguring because of problem with cave: game.install.no_executables_found". There are a few hits, but so far I haven't found anyone with a solution.
Is the problem that there's no good general SWF player for Linux? That's the problem I came to itch.io to solve, so that would be a substantial disappointment.