The drum in that video is a Dynasty DFS14 "Shorty" snare drum. It's basically the same as Dynasty's standard DFX14, but two inches shorter.
I personally wouldn't try to use a sling with a "Shorty", but slings work just fine with the standard-depth Dynasty DFX14 so long as you have a carry hook or angle reduction bar mounted on the drum. The Dynasty P20-DSLR multi-angle bar and leg rest kit would do the trick.