My first observation is in how you state what you're saying. In my mind it says quite a bit about your attitude toward your gf, and your feelings toward what you think your role is in the relationship and it's quite honestly not a positive thing.

Statements such as "I like to have my time on the game to relax" Understandable but coupled with the fact that you then go on to point out just how much you feel you work more and you give a schedule pointing out details of your busy life, it begins to make me wonder if you might somehow feel "entitled" to have the right to ask her to do more and that you have the right to more time to yourself. Almost as though the way you state it is as if your leisure time is more "precious" I see no counter point in how you recognize that she needs down time, I see no point where you're giving her grace and an attitude of providing her but more of a competitive nature in your statements.

I imagine that your arguments can be summed up in a debate of one upping each other and stating things like "but I do this... and this... " followed up by the other partner countering with their perspective on how things really are. it's a problem and I won't condescend to make it sound as if your situation is worse than so many others, because the truth is this is the battle of the ages where relationships only last when couples can get past this.

It bothers me that in more than one point you bring up money and bills and how you pay more than her, pay for the dates. It bothers me because in a true love relationship, one does not chalk up points for themselves to use at a later point in persuading the other to do something more. it's great that you take care of bills and pay her way, but honestly this should be not a game of "if I do this more, then I'm entitled to ask her to... [insert task of choice]. I'm sorry but that's the wrong way to approach a relationship.

I also do not like that when you mention how she handles things it's "she throws a fit"

Take this analogy. I'm a parent and I point out to my kid that I pay for his roof, his food, his everything, he should do more around the house and basically tell him he should be thankful. Does it work? I can tell you without a doubt it NEVER EVER EVER works. Same goes for a spouse, or other SO in a relationship. If we make it seem as though we are doing so much more than they are and try to use this to motivate them to do more for us, it will have the same result. Turn the tables to yourself. What if the more often she gave you sex, that she used that in order to get you to do something more? What would you do? YOu would dig your feet in the dirt more. it's a human reaction. Stop using your caretaker "status" to get her to contribute more.

This honestly goes much deeper and far more needs to be addressed here but honestly I think it's going to take a change of heart on your part to start. Do things for her, pay for things for her, and take care of her, via bills etc because you want to. Leave it at that and that, my friend is how you love your gf. never bring up how much you paid for this or that or the other thing... and make comparisons.