So I'm not sure if this is known already but it was news to me. A Buddy and I were ticked off that we couldn't watch half the videos we wanted, so we did some digging and found a site that installed the Flash program we need. Videos now play just fine! Just go to this page, and click on the link in the first post, and it'll automatically begin downloading. Install it and enjoy!
Adobe Flash disappears from the Play Store today, here's your solution - Android News - MoDaCo
Edit: Here's the link direct: http://mdc.gd/ineedflash