Let’s Play videos (実況プレイ or just 実況 in Japanese) are just people playing video games while commenting.
A few channels I like are:
弟者 from the 2bro channel. Probably among the biggest. He’s got an awesome voice and a cheerful personality, and will sometimes treat you to quotes like 我がクロールに勝てまい！(when swimming from a guard dog)
LayerQ. He speaks pretty clearly. I used to think he was a bit bland but he did grow a bit on me.
Gongen. Plays a lot of NES/SNES games and I think he has a clear and endearing older guy voice.
ToiletPaper Gaming. Another older guy with a pleasant voice.
Afromask. Super clear and relaxed voice. Mostly plays simulator type games.
Toshizo. Nice if you want to practice listening to kansai-ben 
Here’s a super long list of particular let’s play series I personally like:
Honda playing Super Metroid
Naru playing Super Metroid
Blaze playing Metroid Zero Mission
弟者 playing Crypt of the Necrodancer . Commenting in sync with the beat
弟者 playing Machinarium . I find his speech to be the easiest to understand here.
弟者 playing Inside
弟者 playing Abe’s Oddyssee
弟者 playing Little Nightmares
弟者 playing SuperHot
Yumekaki no misogi playing Suikoden I
Gongen playing Super Metroid
Gongen playing Metal Gear
Gongen playing Zelda I
Gongen playing Megaman I
Maelstrom playing WoW
Afromask playing House Flipper
Afromask playing Minecraft
Afromask playing Subnautica
LayerQ playing Ori and the Blind Forest
LayerQ playing Inside
LayerQ playing Hollow Knight
R-Games playing FF7
Toshizo playing Undertale. Kansai-ben listening practice!
Toshizo playing Metroid Prime. More kansai-ben!
ToiletPaper Gaming playing Ori and the Blind Forest
ToiletPaper Gaming playing Megaman 1
ToiletPaper Gaming playing Megaman 2
ToiletPaper Gaming playing Portal 1
ToiletPaper Gaming playing Portal 2
EDIT: Oh, and sorry for derailing, but on the topic of Let’s Plays. @Naphthalene, you speak French right? And you like let’s plays? Did you know of this guy (fellow that goes by the name Noxferan le panda)?
I’ve been listening to him ever since even I started studying French, and for some reason I just love both his voice and character! (More and more the more I can actually understand him. Less so when he swears in English though)