Ah, there's the problem. You burned a data disc, not a movie DVD.
New Macs don't include iDVD because a) most people just upload to YouTube anymore (the wisdom of this is open to another discussion) and b) Apple just decided to get out of the movie-DVD burning business because people HATE how long it takes (with any program).
If you want to burn an iMovie project to a DVD, the correct procedure now is to export it to Export Movie (which produces an MP4 file) and then use either Roxio's Toast or the freeware
Burn program to do the conversion and burning to a movie DVD.
Mac IS the best platform for video, but that's more along the lines of professional video. For consumer video, Macs are still pretty groovy for what people do with video these days (ie, edit and upload it), but not so much for burning a home movie DVD.