Proper calorie intake help please?

Ok, so my BMR is 2122 at 5'9 and 254 lb's. Now I go to the gym 3-4 days a week for an hour each day, 30 mins of weight lifting, and 30 mins of treadmill, so if I multiply my BMR by 1.375 for the 1-3 days of exercise my BMR then becomes 2917.75. Now from my understanding you want to have a calorie deficit of 500 calories to lose one pound a week, I want to lose two lb's per week, so I minus that BMR by 1000 and have 1917.75 right?

Here is where my question comes into play. According to what I said above, I should be eating 1917.75 calories a day to lose 2 lb's a week according to the math, but what doesn't make sense to me is why do I need to consume 1917.75 calories a day on the days I'm NOT exercising?

OR should I change the calorie intake to 2122 x 1.2 (for no exercise) which = 2546.4 minus 1000 for a loss of 2 lb's per week at 1546.4 calories on the days that I don't exercise?

So it would look like this in theory, 1917 calories on the days I do go to the gym and exercise, and then 1546 calories on the days I just rest and don't do any exercise? (On the days I don't exercise I literally do nothing but sit on my PC and play games, and watch TV.)