I can believe he's cheating but I don't consider it probable. Dream's success doesn't come from record settings, so I don't think he has any incentive to cheat.
If anything, I believe more the allegations that his manhunt videos are staged, given that's the interesting content.
He makes money by creating long and entertaining videos (about modded Minecraft and his insane reflexes). This ticks off the YouTube algorithm which measures how much of a video viewers watch and how much time they watch a channel, contributing to exponential growth. On top of this, Minecraft fans are a niche that lives on YouTube.
Dream never became popular because of his speed records, he gained initial traction by creating content on PewDiePie (an infinitely more popular YouTuber). This is exploiting the YouTube's algorithm which recommends videos: by talking about someone famous you'll eventually end up being recommended to their huge user base.