regardless of where the fatigue comes from, cardio helps with all stamina, running doesn't only help your stamina in your legs, helps all stamina because it promotes a stronger heart, better oxygen absorption and more numerous mitochondria.
Right and you can get a great cardio workout by doing interval sprints! In fact, there have been several studies( featured in Bodybuilding.com was where i saw it i believe)that argue the best shape your heart can get in is by doing a bunch of interval sprints with limited rest in between. It is much more beneficial than running a mile at lets say a 8 minute pace. every year i have to go to a cardiologist and get an echo cardiogram because of several issues i have with my heart( murmur, some sporadic heartbeats at times, and some other weird issues they have noticed), and last time i went, which was about 2 months ago, i was told my heart was in tremendous shape. My doc asked me what workouts i have been doing and i told her i was doing some interval training on a treadmill my gym has( this thing is sweet, has harness that prevents you from eating it if you cant keep up, the treadmill can reach speeds of 25mph and up, and has an incline of 45+ degrees). She then told me that my resting heartbeat was at 38, extremely low. She then relayed the same info i stated above and told me this is how to make your heart the strongest. anyways, i will also have to argue that running does help tremendously with stamina in your legs. hell i can squat 500+ pounds multiple times, but if i havent ran for a while and i do a good sprinting workout, my legs will be much more tired than any intense lifting workout i can put them through. i am not disputing the fact that long runs are beneficial to your heart health and stamina, of course they are. but when you look at the sport of paintball, it is mostly short periods of time in which you have to exert a great amount of energy. that being said paintball is really not that physically demanding at all lol.