Assuming the file is downloaded and extracted into your ~/Downloads folder, run the following commands in an open terminal to run the game:
cd ~/Downloads/SUPERHOT_Prototype_Linux/Linux
chmod +x *x86
$HOME/Downloads/SUPERHOT_Prototype_Linux/Linux/*.x86
If you need to, start over and run the following commands in an open terminal one by one to download:
wget http://superhotgame-new.azurewebsites.net/BUILDS/SUPERHOT_Prototype_Linux.zip
unzip SUPERHOT_Prototype_Linux.zip
cd Linux
chmod +x $HOME/Linux/*.x86
Finally, execute the following command to run the game:
$HOME/SUPERHOT_Prototype_Linux/Linux/*.x86

It should now run just fine.
If it doesn't run, please post the exact output from the terminal to show us why so we can help, thanks.