I think the question in the post's heading and the question inside the post are quite different.
"Is it offensive to use 9/11 to market my game?"
I would assume so. There's still people living who directly lost loved ones. I can't predict whether or not people would actually be offended, but it does seem somewhat crass to use 9/11 as a marketing tool.
"Will I get into trouble, or could the game be taken down for being offensive?"
I actually don't know, but I figured one way of checking if it's okay with itch to do this kind of thing would be searching "9/11" in the games section.
I did so and found that there seems to be a few "9/11 simulators", including one that is sold for $1. It is possible that other games may have been taken down for being insensitive, but since these specific games were never popular; they were skipped over.... so maybe itch does take them down if reported? Hopefully an itch member of staff replies to you for a more clear answer.
What sort of does become clear from searching, is that though it is known that 9/11 is considered a sensitive subject, trying to use it as shock content doesn't actually interest people; so I don't think it's worth using it to advertise your game. It might actually work against you since it might come across as "try-hard edgy", so people might be more likely to skip over it.
I tried the your games browser version, and though the mobile controls didn't seem to work very well with a mouse, I did play a bit of it.
I think that finding the right kind of soundtrack could really help. I'm assuming that the game is really intended to be played on a phone or tablet, but I think it's a good idea to do a browser version since it's quite hard to get people to download an Android game from Itch, so a little playable browser teaser might get people interested.
Though it means a little extra development; I would suggest considering working on a mouse option with a more streamlined control system for the desktop browser version, since if you can get people to actually enjoy themselves for five minutes or so and get into a good flow-state in the browser version, they'll probably be more keen to download the mobile version.
I think if you clean up the game a bit, and you really consider what is fun about the game; you'll have a better understanding of how to advertise the game.
Hopefully that's helpful. I actually don't know much about advertising games. Best of luck with your project.