Flash-based websites won't load properly after Flash Player 13 update

Sites like WeTransfer.com, CreditKarma.com, etc. don't seem to be loading properly in any modern browser (FF and Chrome primarily) after the Player 13 update. I'm primarily getting error messages stating that the browser and/or Flash Player need to be update for the site to be used (with a download link provided), yet I am still able to see some of the core HTML elements On my other PC, I'm running Player 12.x, and don't seem to have any issues (please note, but machines are running Windows 7, SP1).

Here's a screenshot of how WeTransfer.com looks after the Player 13 update:

Here's a screenshot of how it looks before the Player 13 update:

I know that others are having issues with video players, games, etc., but this is the first I've seen where entire flash-based websites won't load after a player update. Is there any news from Adobe on when they'll fix this issue?