You can give JonTron [https://www.youtube.com/channel/UCdJdEguB1F1CiYe7OEi3SBg] a try. I know he recently got some bad rap, but his videos are fine.
Dunno if you'd like it but there is Carbot Animations [https://www.youtube.com/channel/UC1uug_uZrVmylfPVBLBvitQ] - the guy does short funny videos based on Blizzard games. He is most famous for "StarCrafts" (based on...
StarCraft) but has branched out into
World of Warcraft,
Diablo and
Heroes of the Storm. Some of the jokes require you to know at least something about the games and some of the StarCrafts are even riffs on the current (at the time) meta in the game, but overall, they are quite good.
It's not exactly comedy, but the channel deserves all the recognition it can get: MrBtongue [https://www.youtube.com/channel/UCI3GAJaOTL1BoipG41OmfyA] - produces very high quality videos about games. Some are about a particular game, some are about some theme or element of a game or games but the guy is amazing. You really cannot go wrong with somebody who mixes philosophers with gaming. The downside is that he uploads very irregularly - there were about four videos last year, for example.
Give Accursed Farms [https://www.youtube.com/user/chilledsanity/featured] a go, as well. The guy did Freeman's Mind [https://www.youtube.com/playlist?list=PL6PNZBb6b9LvDWpI-5CPYUxG1Rnm-vr9V] which is amazing, if you've not seen it. I'd class it as a comedy show but it's also, very loosely, a let's play - he's playing
Half-Life but providing Freeman's voice. It's not
strictly a let's play as he's playing it as realistically as possible and uses cheats here and there to shorten the playthrough by, for example, allowing Freeman to "climb up" and bypass a section. Civil Protection [https://www.youtube.com/playlist?list=PL6PNZBb6b9Lsr6ZnEzRJ5FqBbSYI4rHFj] is a short series set in the
Half-Life 2 world and animated using the Source engine. It follows some comedic adventures of the combine soldiers.
There is also TJ Laser Space Scumbag [https://www.youtube.com/playlist?list=PL975B4642609C30A9] - it's similar to Freeman's Mind in the sense it's very loosely a let's play but the guy doing it has done a complete voiceover of Shepard (first name: TJ Laser) in
Mass Effect 3 and presents him as a hilarious insufferable prick.
EDIT: Now with more samples