If you have to ask if something is satire, then if it is, it's done its job; if it isn't, it's propaganda.
I'm in my late 40s, and Casablanca was always on my radar, but it wasn't something I sought out until I ran into a reference last night and thought "maybe I should finally fucking watch this."
The movie was far better than I was expecting. The writing is tight, the cinematography excellent, and the acting top-notch. I can easily see why it is the movie everything started referencing.
But at this point, damn near every scene has been redone either as homage or satire, making the original seem oddly like the joke itself.
Seriously. Give it a rewatch and try to turn off the voice that says "Oh, they did that in ..."