Did some testing on one of my project pages that has an animated gif: https://cobaltdragon.itch.io/hellsniper
Checking the <img> tag shows 2 gif source files:
img.itch.zone/aW1hZ2UvMzQxOTEwNS8yMDYwNTU5OC5naWY=/347x500/M8Cgy6.gif
img.itch.zone/aW1hZ2UvMzQxOTEwNS8yMDYwNTU5OC5naWY=/794x1000/COX6gh.gif
Checking both files revealed they are single-frame images.
Clicking on screenshot opens the image viewer, in which the gif animates correctly. Checking the source reveals a different image:
img.itch.zone/aW1hZ2UvMzQxOTEwNS8yMDYwNTU5OC5naWY=/original/vDct5H.gif
Using devtools on the project page to insert this image source as the target for srcset="" causes the gif to start animating immediately and the project page appears as expected.
This is speculation, but it seems there is a backend image transcoding system that is rendering single frame gifs from animated sources. I'm sure the itch team will sort it out soon.