It think this linguistic approach remains very superficial in that it only targets vocabulary and ways to represent it and to translate it. It does not tackle the "deep structure" the grammar that underlies and, in my belief, determines everything that sits above. Yes, I know, I'm a chomskian... I also understand that this would have propelled the narrative in a wildly weird area where most spectators would have probably gone to do some other thing than to watch. And "Arrival" is not a bad movie.
I just wonder what would a truly alien language, with a truly alien underlying structure, would look like. Much more than vocabulary keys could be needed to even begin to communicate.
This is also where the SW hypothesis would begin to really become hugely significant.