It's mot GM intrusion, it's part of the plot, and this small short piece is actualy railoadly straight, it just part of the Octagon and it introduces you to The Octagon, The Dogmat and Serenitas, to Keepers, and creating certain knowledge base about The Octagon, knowledge that will help to the party to understand what's going on further. There is big and tricky and complex plot behind, and this is just "video sequence" with few "less optimal" choices.
Do not worry for XP. You will get it in time (hint: after the door?)
And act 2 will have some important and serious choice, and once choice done also picks also pretty straight vector line if we talking about healthy common sense optimal way. Of course it is also influenced by player personalities (by great measure), story and other factors , so there could be "more optimal" way and "less optimal" way, and party will know which choice is which.
In Act 2 the party have very basic tasks - to get understanding of what the hell going on, and to survive and to move to more understandable, adequate place, which could provide some answers.
Act 3 will open HUGETON of options, alot of new mechanics, alot of homebrew stuff. It will be real explosion of information and things to do - it will become quite open-ended, sandboxy, and openworldy with some plot behind . For now for mentioned before reasons it is just the "sequence experience". As i said - there could be many options initially, but as you guess - all things now influenced by "party"s pick of going into certain gate, and things are tied to that choice.
And as for The White - i hope the characters got the hint that this place/entity is not for them - and Dogmats are just ones who hold the gate and just giving the passage, because being obligated to do so. They would act differently without such obligations.
The party entered the Gateholds - and got automatically encounter with people of The White.