Home built in the 60's. I don't believe my washing machine drain is vented. Would this lend to drain backing up before washing machine tub is fully drained?

Home built in the 60's. I don't believe my washing machine drain is vented. Would this lend to drain backing up before washing machine tub is fully drained?

It certainly help. But your immediate problem is a partial blockage in the drain line.I would first snake and clear the drain line. Not having a vent eill slow down the flow of the discharge allowing more build up to occur. You do have options here.
1) you can vent the drain with a AAV, (see image) **OR**
2) you can install a compression fitting on the stand pipe and make it a closed system for the backups. (I have one of these on my own stand pipe)

More questions? I'm as close as a click, Tom