"That guy" is a person who stands out among other people because they do something annoying or inconvenient. They may have reasons to do whatever it is, but most people would choose not to do whatever it is.
For example, someone who always takes the last piece of pizza without asking if anybody else wants it is "that guy who always takes the last piece of pizza".
The phrase "not to be that guy" is a way to acknowledge that you look like "that guy" (you realize you're doing something that some may find inconvenient or annoying in some way), but for whatever reason, you feel something is necessary anyway in a situation, and you don't take the annoyance or inconvenience lightly.
Continuing the example, if you don't typically take the last piece of pizza, but you you can't ask properly because you're starving and late for a very important meeting, you might say, "Not to be that guy, but I've got to have some food, so I'm taking the last piece of pizza."
So basically, you do want to be "that guy", but you want people to think that you don't enjoy doing it so you can beg some social excusal to do it, rather then just outright do it with no apology and clearly be "that guy"...
Yes, you're choosing to do what "that guy" would do, hopefully only in exceptional circumstances. Like with any apology, people who say "not to be that guy" can be sincere or just making an excuse to make their own lives easier.
