The WC always needs a vent. Often you can wet vent it, so it doesn't have to be a dry vent. But in this case that won't work:
The details depend a little on plumbing code. The OP is in MI, which uses the UPC, which requires a vent within 6'. If the run to the stack is over 6', then the dry vent is required for that reason (the bend doesn't matter). Even if under 6', the UPC restricts vertical wet venting to stacks receiving the discharge of 1 and 2 DFU fixtures, but the washing machine standpipe is a 3 DFU fixture, so the dry vent is required. [The laundry standpipe dry vent could be eliminated, as the laundry sink is a 2 DFU fixture, so its vent can wet vent the laundry standpipe, since the stack is already upsized from the minimum laundry sink drain size.]
The IPC has no limit on the length of the WC fixture drain, but it limits vertical wet venting to bathroom group fixtures, so not for a laundry sink or laundry standpipe. It does allow vertical common venting of any two fixtures, but that doesn't apply to the WC, as it has two fixtures above it. [Although again, the laundry standpipe dry vent could be eliminated, so the standpipe is common vented with the laundry sink.]
Cheers, Wayne
Edit: oops, I mixed up my Midwest states, MI (Michigan) is IPC, MN (Minnesota) is UPC.