It can only be that it is viewed that the team gaining control/possession is the same as the player doing so. Nothing else makes sense in this case. Control/gain possession is not defined as the individual or the team; I think it's reasonable to view it as the team gaining control, but that doesn't make the alternative unreasonable. I favour the first.
I don't think that the last blue bit applies due to the "except for the above offences" - if the control/possession happened, then the "except for..." part does not apply.
Interestingly (well maybe), the IFAB document on the changes explains the principles behind the changes, and says this:
The re-wording follows a number of principles:
• football does not accept a goal being scored by a hand/arm (even if accidental)
• football expects a player to be penalised for handball if they gain possession/control of the ball from their hand/arm and gain a major advantage e.g. score or create a goal-scoring opportunity
To me, that implies that the gaining advantage is the principle in question, and that I think that happened with Laporte/Jesus. Obviously, I don't know why it is written like it is, and this is just my interpretation.
I've asked if anyone has seen anything definitive, but all I've seen is people's own interpretation.