So I'm running all over the tiles trying to get the gate to open so I can get the ring, but the gate doesn't seem to want to open. Is there a specific path/order I need to run along the pressure tiles to open the gate or is it just getting them all to light up in no specific order?

The hint just before the plate helps. Just start on one of the closest corner tiles and run/walk along each row of plates until you end up at the door. Like a snake

old dude tells you what to do
super easy puzzle
just walk on them all once without hitting any tile more than once

Thanks! I finally managed to do it XD

start from the right side: up, left, down, left, up... zig-zag the tiles.

Use slow time shout it helps alot

or if you're a mage you can just TK the ring to you through the gate

i just used telekinesis to get it

does it matter which corner you start with if so which corner should I start with?

All you have to do is run over each row of tiles without touching the other tiles. That worked for me, once I had every tile row walked on individually, the door opened up.