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Fortnite's Revolver pistol is a versatile weapon
Don't underestimate the power of the white (common) Revolver pistol in Fortnite Battle Royale. That little gun is super accurate and deals 54 body damage and head 108 damage (based on db.fortnitetracker.com weapon stats). The other great thing about this gun is that it has 2.4s reload time. It's not as powerful as the Hand Canon (Epic; 75/150/2.1s) and not as powerful as the tactical shotgun (Common: 67/134/6.3s) but it has almost triple the tactical shotgun range (8500 vs 3072) so it's a great weapon to pick at the start of the game when you want to get quick kills at close and mid-range, and even some close to long-range kills.
Of course the other uncommon and rare Revolvers are also good and have slightly better stats than the common Revolver (57/114/2.3s and 60/120/2.2s respectively).
In that Twitch video clip that was clipped from TimeTheTatman stream, you can see that the pistol deals decent damage at mid-long range as well Tim eliminates three players with it, one in a relatively long distance, one in mid-range and the other in close range.
The Revolver is probably a weapon that you are going to drop soon after you obtain better weapons, but at the start of the game, any weapon is useful. If you come across a Revolver at the start of the game, always pick it up because it's very versatile due to its fast reload speed and decent damage along relatively long distances. It kind of replaces the absence of shotgun and hunting rifle at the start of the match. When you get either a sniper rifle, hunting rifle and/or a shotgun, you can drop it.
The weapons that you pick dictates how you play. So having a Revolver can pose less limit on your gameplay strategies because you can deal damage to enemies even if they are far away from you.
TimeTheTatman was able to capitalize on this pistol's capabilities in mid and close range. I really liked how he "snipes" with it and is able to eliminate a target far away from him. Just think about it for a second, many of the players in that very early stage of the game don't have good weapons, healing capabilities or even weapons at all. This is why it's important to get every weapon you can and try to get as many kills in the early stages of the game. If you deal damage to an opponent, that player might not have heals and if you meet that player a few minutes later, you will have an advantage.
So overall, the Revolver pistol is a great little weapon, probably underrated but in the right hands, it can be devastating due to its great accuracy, fast reload times and good damage output.