That's funny about the terminology. We call a "chicken gybe" doing a 270 degree tack to totally avoid a gybe.
That's what I thought a chicken gybe was. Letting the boom just flop over is a great way to blow out a block, traveler, or goose neck. The best way to make a gybe go easier is to sail as fast as possible, sheet in, and as soon as the boom starts to flop over, blow the sheet and slow it down before it hits the shrouds. The driver turns down fro the gybe, boom over, and immediately should drive down again. This helps to avoid the round up after a heavy air gybe.
The boat doesn't look that big, but they should probably have a 2nd up there helping out the bowman. We do end for ends on the 36.7 without much issue. It really comes down to the driver and trimmers.
In smaller boats with big mains, it's impossible to sheet the main all the way in b/c it'll round up the boat. So just sheet in as much as you can without the driver bit(hin too much.