I think you're right; this is more about choosing the right license to support your means than a general BSD vs GPL.
I find interesting his point of view compared to his partners': he would have preferred if the code was used by more people, his partners were more worried perhaps about competition (if anyone released a game based on their code, they had to contribute the changes back; which is something id could use as long as they keep that engine GPL).
While your theory is quite possible, it is worth noting
(just to make sure that the premise of GPL is well-defended) that it is also possible his partners were more concerned about "freedom": that their new engine should benefit the commons rather than getting co-opted by people who don't care about end users, and that they would have preferred that their groundbreaking technology encourage more open source games.
I find interesting his point of view compared to his partners': he would have preferred if the code was used by more people, his partners were more worried perhaps about competition (if anyone released a game based on their code, they had to contribute the changes back; which is something id could use as long as they keep that engine GPL).