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The way Kuzuha's playing Splatoon is very correct.
When you're painting over the enemy's paint, you're getting 2x the value. Not only are you gaining territory, but you're subtracting their territory. It's as if your bullets are worth 2x as much. Thus you want to spend the most time possible painting the enemy's territory, rather than filling in blank areas of the map.
Of course, you also get value from filling in the blank areas, in particular places which are highly defensible where the enemy is unlikely to tread. So on your way out towards enemy territory, you can invest some time filling those in. This is the most efficient way to play.
You also have to be wary about pushing too far into enemy territory. If you trade kill for kill deep in enemy territory, they gain the advantage. Because you have to travel further to get back to that same location compared to them. So they basically just got a +1 over you. So you have to recognize which areas are more defensible and be wary of pushing into those. You can bumrush those areas at the end to gain some extra territory before the buzzer sounds.
Also highground is an incredibly massive advantage in this game. You always want to play from highground and prioritize seizing the highground in strategic situations.
