Does 开他的玩笑 mean "he" plays or is played? In the following sentence:


  艾文特别老实、害羞，提什么建议，他都说好的好的；有时开他的玩笑，他会脸红得不知所措，只是憨憨地笑。他喜欢骑自行车，我俩就骑着车在南京城里转，在我这个业余导游的指引下，早到哪儿，逛到哪儿。


Since it starts with 他 as a subject, I feel that it is "he" that makes fun of something, not that he is being. But since the latter sentence makes an impression that he feels embarrassed, so I also feel that he is actually joked at here.

How can I know which is correct? Usually, the sentence should be 他开玩笑 I think, but I wonder if it is actually "he" that is making fun of, why is it in such a form...

Or is 开X的玩笑 different word from X开玩笑? If it is the same and the subject is 他, why not simply say 他开玩笑, instead of 开他的玩笑?
'他的' in '开他的玩笑' is not the subject, it is an  'adjectival phrase' 

开玩笑 = to joke 

他的 = (对)他的 = toward/ about him

'对他的' (toward/ about him) is the adjectival phrase for '玩笑' (joke). It describes what kind of joke it is - 'a joke toward/ about him'

'开玩笑' (to joke) is a single verb treated as one word, but in this structure, 玩笑 (joke) is isolated out and treated like a noun, therefore (对)他的 could be applied to it. 

Similarly:

回家 (go home) is a single verb

in '回[溫暖的]家' , '家' is isolated out as a noun and '溫暖的' (warm) is the adjective for '家'(home)