Science reporting is not great but colloquially people use 20W per <job done> as a way of meaning Watt-hours.
If this is correct, they're saying it takes 20 watts (meaning Wh) to deliver a Litre of water, over three and a bit hours. The time is provided just obfuscated by their "we deliver 0.3L/hour" statement, so by saying 20W/L it does sort of make sense within the context.
~6W/hour (if it means we use a total of 6Wh) would be different than claiming the system runs off 0.1 Watts. Given the size of that solar panel, I suspect they're claiming they are using ~6 Watts for a period of one hour to produce 0.3L. Alternately, they're just flat out wrong and they're using 20 watts for one hour to produce 0.3L.
It could be worded better but I think this is what they're trying to say is that they're consuming 6W.