Seems like that’d be the default assumption - I pay zero point one bucks per kWh, of course it’s an amount. What’s more interesting is kW/h, it feels like a rate but it’s more like an acceleration.
Like he said, it would measure the rate of change between two kilowatt levels. You might ask questions like "how quickly can this power plant adjust the amount of power it's producing?", and the answer would take the form of an amount of power over an amount of time.
This is one of the most salient ways in which different types of power plants differ; it's something that people are very concerned with.