I've never seen a dump trailer that didn't have D-rings welded inside for tie-down points. Some are on the floor / deck and some are at the bottom of the sides (inside) so they don't interfere with dumping a load. Definitely have to secure equipment when towing.
I haven't seen the video you're talking about, but another consideration when loading into dump trailers is keeping the back of your truck on the ground. Some dump trailers have stabilizers/drop-legs that you can drop to keep the trailer tailgate stable so your tractor doesn't lift the trailer hitch and truck rear-end as you climb the ramps. This keeps your hitch assembly from having to manage all that load and potentially popping it off the hitch ball. Even if you don't have the stabilizers/drop-legs/jacks on your trailer, you might already have provisions for them. Sure-Trac dump trailers, for example, have a square socket welded on both sides of the rear of their trailers. The socket is standard, but the jacks are optional. You can buy them from any dealer pretty cheap or make some out of square channel steel. Worth taking a look at your trailer if you don't already have stabilizers and you're loading equipment using ramps.