I did some more testing further to the discussion around here involving @matthias-krutz and @walter-i, and this post on the Movie Studio forum.
I worked out that the VEGAS Stabilize FX does not stabilize video if the top track in the timeline is an audio track. The same issue occurs for me in Vegas Pro 12, 13, 14 and 15. If anyone disagrees with that, please comment.
I reported it to MAGIX, [Ticket#2018032917009074], and added it to the pinned Known Issues post.
Demo: