350kW without any suffix means an instantaneous value, (like 'an electric shower is rated at 9kW' ) but to run the shower for one hour it would take 9kW hours, for two hours 18kWh etc - which is the total of power used or supplied over a time period.
They state 'For reference a Tesla Supercharger provides up to DC 120kW per car' - but each supercharger allows two cars to charge at same time, and if you plug two cars in it can only supply 60kW per car.
A kw is current (amperes) x voltage - which is why pylon conductors, even though they don't look very big and are made of aluminium (a worse conductor than copper) with a stranded steel core can carry a lot of power because voltage is so high (400,000 volts) the current for each KW carried becomes very low (and the insulation ie. air is free, unlike buried HV cables which are extremely complex and maintenance intensive and like a bomb waiting to go off).
Journalists are normally useless at anything technical, and when it comes to statistics they are dire, they will happily tell the public that 'this drug will double your chances of having a heart attack' which would scare most people silly, when they should say 'chance of a heart attack is 1 in 10,000 - this drug raises it to 2 in 10,000' - which clarifies the risk much better.