When I think of the Dilithium Chambers at Maximum, it sounds like he's talking about them being at maximum readiness or efficiency, ready for use.
This is consistent with the Enterprise having multiple Warp Cores, and the Dilithium Chambers probably refers to the Intermix Chambers in the cores, where the matter and antimatter (Deuterium and Antideuterium in TNG, likely true here if that water pipe was the Matter, Deuterium (Heavy Water) being processed before being sent to the Intermix chambers) are thrown together, and the resulting energy converted into a Plazma to power the warp engines.
The glow we see at the back of the Warp Engine? Ionized drive plasma being pumped through the Warp Coils, and being vented after use (being drastically reduced in Engergy).
At least, that's how I interpret things