Back in '82, there were very few American cars with struts. They mostly had wishbone suspension with shocks. And yes, the ball joints back then could have a lot of play and still be in specification. (Dodge for example was something like 1/4 inch.)
Struts are part of the suspension unlike shock absorbers. Struts shouldn't have that much play. (But the test is more sophisticated than just lifting the tire. Requires a dial gauge.). Sounds like the car hit something like a pothole very hard on that side.
If the mechanic shows you both sides and one side is really sloppy, then, I'd take his word. No need for further testing. Yes, replace both sides at the same time.
Struts are part of the suspension unlike shock absorbers. Struts shouldn't have that much play. (But the test is more sophisticated than just lifting the tire. Requires a dial gauge.). Sounds like the car hit something like a pothole very hard on that side.
If the mechanic shows you both sides and one side is really sloppy, then, I'd take his word. No need for further testing. Yes, replace both sides at the same time.