First - realize that there are times when it's optimal to make demands on a team that aren't respective to exactly who does what. Making exceptions for a specific individual sends a message, and it may not be the message your boss wants to send. There are certainly times where as the boss, I could see a chain reaction across a team where I wanted to strongly send the message "you're all in this together, not matter whose problem this is, you are all on point for making sure that all of our work comes out well".
Second - so I advise asking, but starting from the point of awareness that the first point could be a factor. One way to start the conversation would be to casually point out any relevant fact you think the boss might be unclear on and then ask how you can be of assistance on the day that he's told you to be available. Something like:
Hey! I had a question about the not-day-off and the issues on our site. I work entirely in the mobile app and I don't have access to, or insight into the ways we fix issues on the main site. I'm totally glad to be here to help - but I don't know what I can do to be of assistance here. I'm afraid that I'm mostly a distraction to the team, because all of my interaction with the site folks has been around the mobile app, which doesn't seem like part of our big problem. Is there something I can be doing to help here? Is there a way the mobile app side can help or something I should be specifically focused on to make the work of the site team easier?
If the answer is "yes" - then you'll learn how your work fits in and how you can help. Or you'll learn how the boss completely doesn't understand what you do or how you fit with the team that's having the problem. Or you'll learn that in times of crisis you are expected to pitch in, regardless of what you regularly do, and what that would look like.
If the answer is "no" - you have a good transition point into "then why I am being denied vacation time if I'm just going to be in the way?" You might not even have to ask, the boss may immediately say - "Oh, I didn't mean YOU! Feel free to not show up, but don't make a big deal of it"
Either way, you come off as a person who thinks first of how to be helpful and only asks for special dispensation when it's clear that your sacrifice doesn't really help anyone.