Wait a minute, I do still use the stock browser but it still won't do the ESPN videos. It always says I need Adobe Flash even though I do have it installed. Oh well.
I don't know if it matters, but are you on the mobile site or full site? I just went to ESPN on the stock browser and watched a video on ESPN.
Although, I pulled it up in Chrome (mobile site) and it played the video too. So maybe I don't know much after all.