There were templates around for videoshare sites. Check with http://www.nuevolab.com/template to see his templates will work.
Doing a custom theme is possible, but takes a lot of time and therefore costs more than if you find a template for sale. Media share features already include mobile ready playback.
Mobile templates that are responsive, are best created as separate pages. I did some adapting for mobile on a customer's site. There was a mobile template available for an older video software site called "iPhone / iPod - Mobile Webapp Module Version 2.0." Ask Mediashare admin if it is still around. I can't find it online anymore.
A couple of adapted pages for smartphone playback, I did for a client look like this. This is up and running on popmodal.com for group pages and user pages.
This lower one is based on the iPhone / iPod - Mobile Webapp Module Version 2.0. So either buy that code mod, if it's still available, or we would have to make a new one from scratch. This page works when it is played on a narrow page. This is up and running, but you need to be a member to access the mobile page.
The above examples are all web, not an app inside the phone. That would be a different development project and probably too expensive. Be warned that customizing a complete new page look that works for responsive design is time consuming, and there are a lot of choices, testing and design problems. Something can seem good, but when you test it you run into issues. It is a big project to get right. You have to be prepared to spend time and money to do it. It is much easier to find an existing tested template. Even at several hundred US dollars, they can be a good deal if they do what you want.
Hope that helps.