I noticed in the movie that the GSX service vehicles popped into view as needed...
Thank for the question, which gives me the chance to illustrate how complex GSX really is...
If there is any way that problem can be eliminated it would, to me, be a huge reason to buy GSX. I would imagine that it would not be an easy thing to do but it would add exponentially to the realism of the sim+GSX.
Possibly inserting the appropriate service vehicles in their logical places at the user AC's assigned gate well before the user's AC arrives???
That's exactly how it works...

In the video, the airplane started already at the gate, which is why the vehicles popped up.
However, even if you start at a gate, not all vehicles pops up like that, only those that are usually placed very close to a gate, which we called "parking services".
Other vehicles not shown on the video, which are not usually parked very close to a gate, like the Catering vehicle, the Passengers bus, the GPU, the De-icers, don't pop up even if you start at a gate, but they follow a path from a parking stand of "vehicle" or "fuel" type (if the AFCAD has it) or any random parking in that area. It's only the passengers Stairs and the baggage loader which pops up and only if you start at a gate.
BUT...
That menu you saw on the video was the "parking" menu, that appears when you are at a parking stand with engines off. If you just landed and are taxiing to the gate, the in-game menu wil be different, showing options to select your parking and, if you want, being guided there by a Follow me vehicle. Once you told GSX your destination, it will immediately prepare the parking with the needed vehicles, so you won't notice any popup and, if there's a docking system will place it and if there isn't, a marshaller will wait for you. This for the "close to the parking" kind of vehicles. All the others will always have to reach the destination parking by travelling, possibly even a long way, depending on the airport.
Of course, all travelling vehicles will respect the "vehicles" paths in the AFCAD so, if the AFCAD has been made correctly, they'll follow a realistic route. In absence of proper vehicle paths, they'll just use the regular taxiways network.