MPEG TS is used primarily to broadcast digital transmitted TV (DVB, ATSC, DTMB, SMB, ISBN, etc.) as MPEG-TS is designed to be very robust and can easily "survive" bigger outages in the signal.
So you finally got the recording features to work on your DreamBox, but you want more? 🙂 If you only want to view the MPEG livestream file (.ts) then use VLC player, which is the best player around. But if you want to convert the .ts file to eg. Mpeg 2, or MPA/MPV format for [...]