Although the explanation of how it all works is rather inconsistent in Stargate. Initially, gate travel was something that people experienced and it was only later changed to being dematerialised.
It definitely is explained as described above. The gate itself, the “event horizon” is all part of the apparatus for accessing the wormhole, not the wormhole itself. I forget the episode, but there is one where something happens due to the fact that they recreated/reverse engineered the “brains” of the device with human design (missing some key failsafes) and some of them get stuck in the “buffer” (dematerialized state) until it’s figured out how to reconstitute them.