You got me curious so I just looked.

My ancient Maytag washer has a clamp for a ground wire on the back. My water supply has a clamp and a ground wire on it (pipes are copper in this 1962 house.) I don't remember when I bought the washer but it was probably around 1992.

Second thing, we've never confirmed the OP washer is plugged into a three prong outlet. It very well might be a two prong and they've used an adapter.. The reason I bring that up is some years ago I was working in a paper factory and I got a shock from one of the office computers. The outlet was wired backwards, there was no safety ground (they assumed the conduit was enough, but it wasn't), and the case was hot. Hooking up a cable I had one hand on the computer and the other on a grounded connection, and I got that old familiar tingle. The PC ran fine hooked up either way.