The thin piece of metal may be worn a little. Just recently I changed the front sprocket on our 200x and the new one still has play in it although not nearly as much as the old one. Your new piece will have some play in it naturally but if it's more then it was with the old one I would say that the old one was kind of worn in to place if you can understand that.
Trikes
1984 Honda 200x, 1984 Honda 200m
Bikes
1995 Honda CR125R, 1985 Honda XL100 (gone), 1982 Kawisaki KZ550 LTD,
2001 Yamaha TT-R 125L, 1983 Honda XL185S (current project), 2001 Suzuki SV650S