You might or might not know that Chicago does not allow the use of PVC in any space below ground level.
I might be mistaken, but it looks to me that those 2 stacks are both drains. If so, you cannot connect to either of them for the purpose of a vent, unless you do so above the flood rim of the highest fixture connected to the stack.
There is nowhere there for you to make a proper drain connection for a washer standpipe. You would need to break the floor and make the connection to the horizontal drain. Again, in Chicago, this would all need to be done in cast iron.