You may receive this error in certain circumstances: "It seems your browser does not support running Unity WebGL content from file:// urls. Please upload it to an http server, or try a different browser.", but you can get around it. You may be able to download and play from within the itch application on Windows, but you will receive this error if you try to open the downloaded files from your Windows file system instead. However, you will also get this error if you try to download and play from within the itch app on Linux, which is more inconvenient and is how I ran into it.
This requires having Chrome/Chromium installed.
On Windows, create a new shortcut to Chrome and modify its "target" parameters to something like this, but with your own path to Itch games:
"C:\Program Files (x86)\Google\Chrome\Application\chrome.exe" E:\Programs\itch\monsamsara\index.html --allow-file-access-from-files
This will also work from within a cmd terminal.
On Linux, I created a mon_samsara.sh shell script with the following and set it to executable:
chromium /home/my_user_name/.config/itch/apps/monsamsara/index.html --allow-file-access-from-files
These are all on one line in case that's not clear.
Of course, the other option is just to play from the itch.io website, but if you want to download the files, this is how to do it. This should also work for other Unity WebGL games.