I think you may have misread Tarheel's post #4. He was saying that you shouldn't use those kinds of things to talk about games and gym wear, since they belong to different kinds.
Thank you so much for this. So, for similar things we say that kind of thing/those kinds of things. For example:
1) As a child he used to play with girl toys like beads, jewelry and those kinds of things/ that kind of thing.
I wonder if it's possible to 'things like that/stuff like that' here?
And, for different kinds of things we say things like that/ stuff like that. For example:
2) As a child he used to play with bids, barbie dolls, doll houses, guns and things like that.