The size of the aquarium is important as a larger aquarium allows for more separation between individuals. With more space, territories become larger and the chasing less intense. Hiding places provided by such things as driftwood, plants, rocks and other decorations will also help. Distractions such as other fish to chase or that might harass the gouramis would also help. If you don't consider the environment in its' entirety any answer would be meaningless. The chasing becomes less relevant if the "chasee" has a place to hide or the "chaser" has other distractions.
As an example, I have 4 pictus in a 410 gallon aquarium. They harass each other constantly.The aquarium is chock full of hiding places and yet they all live within a 2 square foot chunk of space on the substrate. They never hurt each other but they do love to fight! They have many other neighbors to cope with and their space has lots of plants and driftwood to create individuals niches for each fish within the space they have collectively staked out. But they prefer each others' company to the loneliness of being alone and without the aggressive interaction. Go figure!
If you want just a simple answer, yes that male gourami is quite capable of killing the female. We are all just trying to be more helpful than that. I guess we just figured you knew. Sorry.
Beasts