IF you want this to pass code, the WM pipe must be 2"...it cannot be 1.5". The WM outlet is pumped...it flows much faster than gravity would normally have water draining. With today's WM, you'll often have problems with an older (before they changed the code) 1.5" pipe - it will back up and overflow. Now, if the sink is lower than the top of the standpipe, it might just find that easier to drain into! If your existing WM doesn't have problems on a 1.5" pipe, when you do replace it, expect you probably will.
Important note - I'm not a pro
Retired Defense Industry Engineer; Schluter 2.5-day Workshop Completed 2013
doesnt the fitting in the bottom photo look like a vent T?? where in fact it should be a wye and an 1/8th like in the top diagram?
Not saying your setup should be like this top diagram just pointing out the use of a wye and an 1/8th