I think people will likely dismiss your marketing as rage bait or otherwise have a worse first impression of your game, so I don't recommend it. I'm sure you'll also get into trouble for doing it.

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.

Very very poor taste. I take it you were born after 2001 otherwise you wouldn't be asking such a question. People lived in fear about what or where it would happen next. I live on the other side of the world but I remember the day vividly as an 8 year old. I have visited the memorials in New York aswell. Think about how somebody would feel if their families members died on this day or still suffered the effects. I'm actually shocked you would even consider the twin towers as a form of advertising.

Low blow  to use this imagery to advertise  Very low.