Is there an easy to understand explanation on how the ball goes forward towards the net when the swing path is almost parallel to the baseline? You would think the ball should fly towards the side fence instead of the net.
Is it just the racket face angle at contact or anything more significant to it?
The meanings of word descriptions of tennis strokes are the subject of many threads, 50%? You can search back to the beginning of TT and see very similar threads as many posters have various undefined tennis terms to use in very similar threads.
See the thread
Junior Twist Serve. The OP's serve is compared to Stosur's in a clear high speed video. They were very close in racket path.
"Swing path is almost parallel to the baseline" is a misleading simplification for what you see in the videos and the Frank Salazar kick serve taken with an overhead camera view. See Toly's composite picture of Salazar's kick serve for the hand or racket path of a kick serve and its angle to the baseline. Unfortunately, those overhead camera views are hard to find.
The racket face is tilted at about 14 degrees
closed just before impact for the kick serve - much more than for the flat and slice serves.
Many posters remember tennis terms that are show-stoppers when it comes to describing and understanding the 3D complex service motion.
I can't remember what servers do in spatial detail, but I can view a video and see what they do in a few minutes.
The above discussion is limited to before impact because it is easier to describe than after first touch.