it's not very clear in the first video how far away he is firing from. it may only be less than 2 meters - it's certainly not 4 or 5. the first BB he fired at the paper target didn't even penetrate the paper -- i am not sure he is having as much "success" as you think he is.
there are a couple problems -- the caps are probably not very uniform in charge, so you won't get a predictable amount of force propelling each projectile. the BB's he had also varied in diameter a lot, as you can see by some of them fitting snug and others not. too snug, and the force from the cap has to work against friction just to get the BB into the barrel, and too loose, and the force of the cap will blow around the side of the BB, so again the variability in your range is large. also if you use tissue paper like he did to make up for a small diameter BB, the force from the cap is going to be unevenly distributed, so the projectile is unlikely to be able to be aimed effectively and will have a greatly reduced range compared to a snug-fitting BB as a lot of the force will be expelling the tissue instead of the BB. the tissue will cause a lot more friction too, slowing down the BB. i wouldn't do that - just don't use small BB's.
i would assume that the capgun is also not manufactured well, so that the barrel s not very straight and/or has nicks inside it. this is going to make you inaccurate and add variability too. another problem is the gap between the barrel and the chamber - a lot of force will escape to the air when the BB passes through that, and not in a uniform way - which will slow down the projectile and do it unevenly, introducing spin. spin is good when it's controlled (by rifling the barrel) but not good when it's semi-random. if you can fiddle with the actual gun to snug up the chamber to the barrel it may help.
honestly any $20 actual BB gun is probably going to be more accurate and have better range. . . from the vid either he's a very poor shot or the gun is wildly inconsistent. it's pretty hard to be a good shot with a bad gun. i'm going with wildly inaccurate gun, because i don't think he's very far from the target at all. it probably wouldn't even hurt to get shot with that from more than 2 meters away. don't go pointing it at anyone regardless!
you might try some WD-40 on the BB's - i wouldn't use motor oil; it's relatively heavy. and you might try taking apart some of the caps and doubling up the charge to get more range. still, i doubt that thing is going to be very accurate at all, and probably the #1 problem is getting BB's that are uniform size, #2 is the pistol itself, chamber and barrel, just not being very straight and true.
