Works fine for me. The version in menu is 1.3.7011.41203, the same as on download page.
Found a solution.
So basically the game gave me an error saying it failed to find "/home/my_user/.config/Owlboy/config.cfg"
I proceeded to create a blank file manually in the specified location, lo and behold the game runs. Can confirm it does say 1.3.7 in the main menu :)
That's fixed now. Please download the new version: owlboy_1_3_7011_41203_hotfix_28163.sh
That fixes the missing config.cfg file issue.