According to Google (https://www.google.com/search?q=define+astronaut), an astronaut is "a person who is trained to travel in a spacecraft". It doesn't say you have to "add" to the mission.
According to that definition then someone who is trained and never leaves the ground has more right to that name
than someone who pays $250k to be a passenger on a spacecraft. I don't think being called an "astronaut" should
be the goal but rather that you've been to outer space.
Personally, the description of what you're buying, to me, leaves a lot to be desired. Before I would buy a ticket,
I would want to know there was ample time to experience weightlessness and take pictures out the window.
Does anyone know exactly how long in space you're actually buying? It sounds like a quick up and back down
with maybe a few minutes of weightlessness. To me, that's barely worth it at free. I would want to spend at
least an hour if not 24 hours. Less than an hour and there are cheaper options like the "vomit comet".