I don't have a steamOS device to test with, but I'll try to ask around. I thought the linux build would run just fine. Was there any error displayed?
Looks like a permission issue? I don't know if SteamOS has a "run as admin" option, but if it does, you can try that.
Or in the console, try to enable execute permissions by going to the game directory and iputting the text below without the quotation marks:
"chmod +x Toe II Toe"
Since you shouldn't really just type in random commands in the console given by strangers, here's a bit more info/reference and what it does (https://www.warp.dev/terminus/chmod-x).
After that, try running the game. Let me know if that works!