Doxy.me uses WebRTC for video, which Internet Explorer currently does not support. Internet Explorer is currently being phased out by Microsoft in favor of Edge, which does support WebRTC. So it is possible sometime in the next year or two you will be able to use the Edge browser.
In the meantime, you can use Google Chrome, Mozilla Firefox, or Safari.
If you're using iOS mobile devices, you can download and use our lastest iOS version- http://itunes.com/apps/doxyme
If you are using an Android device use just need to use your Chrome browser on that device.