The Ventapipe won't fix it.
There's a blockage (almost total) downstream, possibly behind the board with the socket on where the pipe has an elbow to go out through the wall or where it drops into the floor/ joins other pipework.
There may be an access point behind the board to use the snake in or if not take the left trap off and push the snake down from there.
When the water starts to flow keep twisting the snake around and run water down to clear the blockage (grease) off the internal sides of the pipe.
If it is grease the snake will push through it and when pulled back the hole in the blockage will close up again.
The P trap vents are to let air in to break a syphon caused by flow past the end of the pipe lower down.
The Ventapipe does the same thing.
What you are doing by releasing the vents is to let trapped air out and allowing the water to drain out through a very small hole in the blockage.
Using any chemicals on the blockage is only removing a very small amount of it, hence why the water stops running away