It is very possible. Washing machine the those days didn't expel their water nearly as fast. If the drain line is galvanized steel, it could be corroded as well. If it was mine, I'd explore starting with the standpipe. If it is 2", it is unlikely they would have reduced it as that is a really big no no in plumbing. If the stand pipe is 1-1/2", then you would need to see if it goes into a large pipe and where. If you are lucky, it would just be a small stand pipe and would be fairly easy to change to 2" without major plumbing changes.