Ok. you have 2 problems there.
1. You have your ground and + Mixed up on your diagram.
2. The Xbox controller is only giving off 3v and your using 5v leds.
The Xbox controller has 2 AA 1AA = 1.5v, AA+AA =3v
In these Photos im using a 3.3v 3mm blue led.
Sorry Pics are so big didn't feel like resizing lol
Directly to battery with 3.3v led
Hooked up to those points with the controller turned off. With the positive and negative switched from your diagram.
Led when controller was turned on
When controller was turned on but ROL was on sry cant really see the led that well in this pic
Idk how to get the leds to light up brighter because the only leds iv hooked up to a controller were rumble activated and that gave off enough power for for the 3.3v leds but what im guessing what you can do is get some lower voltage leds and try it again.
Hope this helps. good luck