Dunno if you realized this yet, but this was Dalinar himself. He was set up earlier as being able to speak as the storm and override the Stormfather the first time he rode as it. And while Kaladin didn't seem to make the connection (likely, Dalinar doesn't sound exactly like himself), Dalinar himself confirms he was the one speaking to accept the Words in his next POV chapter. It's pretty obviously setting Dalinar up to inherit Honor's power directly though his bond, as the Stormfather keeps expressing how his powers seem to go beyond that of a normal Bondsmith. But I do agree the things specific to Kaladin seems significant too, and there's likely something else at play here. It could go either way.
Yeah, I realized that after I posted it and went back to reread. And yes, it's been moving towards Dalinar inheriting Honor's power for sometime now. It's interesting that Cultivation has directly intervened with three characters we know of...Taravangian has assumed Odium, and Dalinar may inherit Honor. Lift hasn't been super important yet, but I wonder what Cultivation plans for her. Possibly replacing herself? We know she had a relationship with Tanavast, but not a whole lot more.
The son of Tanavast thing is going to be significant for something, I'm sure. looking forward to seeing why that is.