The oars move more than a little through the water. It isn't the immutability of the water that allows for traction, it is the drag, or perhaps resistance is a more appropriate term, that gives bite to the oars in the water.

What do you mean?

I suspect his point is that the blades of the oars, when immersed in the water, don't move (much) relative to the water. Approximating the blade as stationary in the water, we can see that the boat moves because of a lever effect. If the oars moved freely through the water there would be no thrust, as would be the case when rowing in liquid helium.

However, given the context, it seems a singularly pointless nitpick.

Especially considering that, in practice, oars move quite a lot through water. It’s fluid, after all; rowing is not like ski-poling yourself along.