Why is 讲 where it is in 他英语讲得很好?
Maybe "他讲英语讲得很好。"? And the explanation is that the first 讲 is just left out?


Exactly this.

The grammatical rule here is pretty simple, but sometimes overlooked: 
with complements of grade (得 + verbal phrase) the main verb is doubled, in order to keep the strong bound between verb + object and between verb + grade particle, so your example would be actually written:


  他讲英语讲得很好 


Then, the first occurrence of the main verb (the one before the object) can be omitted, so you end up with:


  他 (subject) 
  讲 (main verb) 
  英语 (object) 
  讲 (verb doubled) 
  得 (grade particle) 
  很好 (verbal phrase)