Embarrasingly enough I didn't have a very clear picture of Griezmann as a player when he arrived, despite him having played on top level for 10 years.
I looked at him as a pretty quick, good finisher who is pretty good on the ball and is used to work relentlessly in both defence and offence. I also remembered him playing more of a playmaker role way back, and so imagined he was intelligent both on and off the ball. I saw him as a late replacement for David Villa. 
This was evidently very far from the truth. If he is an 'intelligent' player, it is a very different type of intelligence than what Barcelona needs. 
So far, we've only sometimes seen glimpses of great technique from him in isolated situations, and he also does work very humbly - he runs a lot, even if it usually is in the wrong direction at the wrong time and in the wrong speed.  
I think he is coming close to being the worst player in Barcelona in the last 15 years - he gets so much playing time and offers so little. Always in the wrong place at the wrong time, making more easy mistakes when playing simple than Dembele but at the same time offering nothing in terms of doing the "hard things". He is "good enough to be bad enough".
I guess he does play a simple tactical role in Koemans system, holding the opposing defence pinned.