The layout is correct. What you have is an "Island" vent for the kitchen. The vent goes up as high as possible and then drops back down and reconnects to the waste below. Before the connection of the two is made, they would have pulled off a foot vent that went up a different wall and up through the roof.
Normally the waste from the santee that holds the p-trap would be 2" on the vertical.
Yours looks to be all plumbed in 1-1/2" black ABS. I don't know how they size in Canada, so maybe that is all just fine.
The drain from the dishwasher will high look to the counter before it enters the wye. That's normal too.
Here in the States, we would either high loop it , or use an air gap fitting on the counter. Again, that's a local code thing.