No.
kW·h or kWh is kW times hours.
kW per hour would be kW/h.
Notice how the Wikipedia article uses “annual” or “per year” in connection with this unit.
When you buy an appliance, the shop or the data sheet will usually list how much electricity the appliance uses within a year measured in kWh, because that’s the unit also used in your electricity meter (how could that go up constantly if it was kW/h) and when you pay your electricity bill for the year so you can easily calculate the impact of the appliance on your electricity bill, and if you have a look at that, then indeed
It does if you want to use less energy.
It does not always if your priority is on saving money overall, depending on whether the energy cost savings over time make up for the price or price mark-up for the more energy-efficient appliance.
And it does not if you scrap a perfectly fine appliance just to get an energy-saving one, because … Ok, we’re Fairphoners, we know why 
.