The gatehack shown in the video speeds up the route by a few seconds. Most full-game runners run into the gate before doing the gatehack to make it more consistent.
The level is very straightforward, except for one tricky jump in the beginning. If Yoshi hits his head on a wall, you can simply continue to hold down jump and he will automatically perform an additional flutter. This can be used to easily navigate into the hole shown in the animated gif below, to skip riding on the moving red platform. A faster but more difficult way to do this in shown in the IL record.
The warp is performed by holding left when bouncing on the arrow, as shown below: