Browser-based games now open identical, function-less new window when 'Run game' clicked if browser cookies disabled (Firefox)

[chocmake]

Describe the bug
When 'Run game' button clicked a new window is opened in Firefox that displays the same page content but the game doesn't run.

When cookies are enabled the secondary window instead launches a different URL, one at itch.io/embed-upload and the game loads and functions.

I know at least with this game that I'd played months prior in Firefox with cookies similarly disabled it didn't exhibit this behavior (and ran instead in the same origin window), so both the new window opening and the game not running when cookies disabled seem to be new behavior.

To Reproduce
Steps to reproduce the behavior:

1. Block all browser cookies in Firefox's settings. This can be done by filtering for 'cookies' and choosing the 'Custom' option (selecting 'All cookies'). This preference allows the user to selectively enable cookies on domains.
2. Go to eg. this game's page and click 'Run game'.
3. Itch.io launches a secondary window with the same itch.io URL and 'Run game' button but nothing else occurs. Clicking the button again will launch another identical window and so on.

Expected behavior
On Chromium-based browsers (as of writing) the game runs in the same window as was open originally but since in Firefox the game launches a separate window and doesn't load if cookies not enabled for the site it would be worthwhile notifying the user that cookies are now required.

Desktop (please complete the following information):

• OS: Windows and Kubuntu (Linux)
• Browser: Firefox

Additional context
I recognize that cookies being selectively enabled doesn't represent most users of the site (and that some games don't handle the lack of eg. writable local storage) but posting a ticket either way since the behavior seems to have changed from a few months ago.