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You said the literal opposite of what you later explained. "Always toward the center" = direction does not change.
Did I? I was thinking in the sense that when climbing a steep hill, gravity isn't actually any stronger, you're just fighting against it more, since you're travelling more vertically than normal. "Vertical" on a flat disk would be basically toward the edges. Falling there would be the same as tumbling down a mountain that gradually slopes to flat ground, but you'd still experience the same gravitational pull, no?
It seems he edited his comment. "Always towards the center" means the direction of gravity, not it's magnitude, absolutely would change. Most of the mass of a disk is towards the center, rather than the edge. That's why gravity would pull you that way, but not with any more force than it would push you downward against the ground at the pole. As explained in the video, standing at the pole would feel totally normal (i.e. gravity is pushing straight down). At the edge, it would feel like hanging from a vertical surface (i.e. gravity is pushing sideways). If I'm not mistaken, that's completely in line with what I said before. If anything, I suppose it's possible gravity would be slightly weaker at the edges, just like objects in LEO don't actually fall at quite 9.8m/s, it'll be just a little slower, but that wasn't covered in the first few minutes of the video, which is what the scope of my comment referred to. Without actually leaving the surface of the disk far behind, however, I'm not sure the difference would be appreciable.