Hi, just to let you know, I had the same issue with 1.5 on Elementary OS 5.0 (Ubuntu 18.04.2 based) when downloaded through the Itch desktop app. Wouldn't launch through the Itch launcher, and trying to run it from a terminal gave me this output:
bash: /home/michael/.config/itch/apps/laigter/laigter-1.5-beta-x86_64.AppImage: cannot execute binary file: Exec format error
Version 1.3 from that download link worked fine, so I went to the Itch website, and downloaded 1.5 through Firefox, instead of the Itch desktop app, and this time it worked!
So the issue might not be with your .AppImage, but with something that happens to it when downloaded through the Itch desktop app.