A toilet in the basement drains to the floor with no vent in sight. There is a vertical "wet" vent about 15 feet away that drains (among other things) a third floor washing machine. It also vents out the attic roof.

When the washer drains, there is gurgling and swirling in the cellar toilet bowl. Does this indicate poor venting? Or is a constricted drain beneath the concrete a more likely cause?

Thanks.

This question belongs on the plumbing page. I almost missed it.
A washer pump discharges with much force. Add a three story drop to the equation and you have a lot of water dropping very fast down the stack. This discharge sets up a suction that's relieved by the washer vent. Some of this suction is picked up by the bowl level in your toilet.
If this just started I would say the washer vent has a partial blockage but if this has been ongoing from day one I would have to sat that this is a normal reaction to a heavy discharge dropping three stories past a wet vented toilet.
A "gurgle" indicates suction. When you should become concerned is when the toilet starts to "bubble" and back up. That indicates a clog in the line downstream from the toilet. So far I don't see a lot to be concerned with.
Good luck Tom PS. If you have a plumbing question I suggest you post them on the plumbing page in the future.