I was just working on a Chinese review app and came across the sentence:
And I was wondering if the doubling of the first character is unique to certain kinds of verbs or all 2 character verbs.
Or can I also say 他游泳得很快。?
I agree with comment 1 & 2.
游泳 is Separable Word(离合词). There are some other 离合词: 吃饭， 睡觉， 散步， etc.
The grammar here is that 离合词 can not be followed with an object or a complement directly.
You should also note that not all two-character verbs are separable(离合词), hence follows the rules above.
This is mostly just for clarity rather than anything else.
他游泳得很快 is not okay but 他游得很快 is okay. Without any context though who could understand a random
他游得很快? No one, really. Hence we get our doubling up: 他游泳游得很快。