Hmm, which version were you using before? And is the new version that itch tried to install the same architecture? In any case, you can probably fix this problem by explicitly uninstalling all versions of Tiled (also check Add/Remove Software in Windows) and then installing the latest one.
I was on 1.1.2 before, and I actually I'm not sure if it was the same architecture...I think it was.
Yeah, I ended up doing an uninstall...but itch's uninstall also didn't work. I ended up just deleting the "local files" of Tiled, mashing uninstall a couple more times, and then reinstalling -- which eventually worked.