I'm afraid it's not correct, although we can understand what it means. That pattern only works for transitive verbs, like 看了一小时电影，听了半小时歌，there must be objects after the verbs. However, the entire 游泳 itself is an intransitive verb. 游 and 泳 are both verbs and both mean swim. It's better to say: 他游泳游了一个小时。

Yes ,if u wanna express how long you did sth,you could say 1. V+time+O 看1小时书/打1小时篮球 2. V+O+V+ 了+ time 看书 看了1小时/打篮球打了1小时

I would add "的" between "一个小时" and “泳”。 So the full sentence is “我游了一个小时的泳”. Because "一个小时" is a attributive, which is used to limit or explain nouns after it. You swim for 一个小时, not for 两个小时 or whatever. "的" is similar to 's in English, for example, one hour's swimming, two hour's drive. So it sounds more natural when you say “一个小时的泳”.

Thanks

I think if you say"他游了一个小时泳", people can understand it, but it's better for you to say"他游一个小时 or 他游泳游一个小时. I hope this helps!