@ Tess_Sluijter
Well, I will agree here that the wording (or what is said) might be improved; nevertheless, let me try to clarify this a bit.
First of all, let’s start with the agreement that we are only discussing here a standard, vanilla production-ready system. That is, not a system set up specifically for testing or development and one that fully complies with MongoDB production-ready recommendations. (That’s basically what’s being shown in the lecture). And we will assume that the MongoDB is version 3.6 or later.
Now, to address your various points. First of all, there is a “primary shard” on every sharded database. See the definition here if you’re not familiar. This will be different than the primary of the replica set(s) for the shard(s).
Second, as the documentation here describes, the sharded cluster does use the primary shard rather than the mongos as a place to perform some operations. In general, the final integration will occur on the mongos before routing the documents to the application, but sorts in particular are usually done on the primary shard – although, as you can read, aggregation sorting may not be. (Yeah, well it’s not really that straightforward. 
)
All of these are fairly advanced concepts and, as described in the Lecture, intended to be mostly transparent to the application and developers.
Finally, with regard to this being “outdated”, these are all fairly new courses and I would suggest that you assume that the information is current. If there appear to be difficulties, then do by all means post your questions as you have here – we’ll be happy to help.
