Reply from IR on why the new Interactive Videos on Twitter play differently on Mobile and Desktop. On the Desktop, the videos will load and play within your Twitter Page. On the Mobile version, Twitter itself open a full screen to Open the Video. Here is the response.

"Thank for your support. New rollouts are exciting. Please note that the video in general doesn't work the same way on desktops as it does on iPhone apps but that is a limitation of Twitter, not our system. It is the same way with YouTube or anyone else."