Sorry, but so few people use our sites with Windows Phone that the amount can't justify spending time and work on supporting WP (unless it's a very easy and obvious fix).
In this case however, it was indeed an easy and fairly obvious fix: The scrollable area is a <main> element in the new mobile chat, and that element doesn't really exist in Internet Explorer. But it can be made to work just fine by explicitly making it display: block, which is what I did.