I am sure that you are only going by what your source of info said but that particular author has some points of fact that are not correct. Keeping male and female domestic betta splendens (which is what your type of betta is) is just asking for the death of one or both of your fish. These are solitary fish and prefer to live alone. Males and females will stress each other out if left together which lowers their immune system enabling disease to take hold. That is if the fish live long enough for that to happen. Female bettas are quite aggressive and a lot of the time they are the ones that kill the male and not the other way around when together. Females kept in groups will "mob" attack a male. Sometimes this aggression between individuals will happen immediately and other times it may take a little while but it will happen. There is no such thing as "playful" aggression (chasing, fin nipping) with this type of fish. Normally you are lucky to see the aggression before a fish is killed.
Keeping your bettas in this small of a tank is basically cruelty in my opinion. 2 gallons per individual betta is pretty much the minimum for anyone keeping bettas as pets. I do not recommend dividing a tank of less than 5 gallons and only for maximum of 2 bettas. The stereotype that they do not need room to move because they are "lazy" or "inactive" is just outright wrong. They need space just like every other fish and when given space, they will normally use every bit of it. These fish require a heater to keep the water temp no less than 78F and to keep it stable unless you live along the equator. Water temperature is always a couple of degrees or so less than room temperature and will fluctuate especially at night when the temperature goes down. Low temperatures and changing temperatures bring on stress which in turn will bring on illness. In theory, bettas being anabatoids do not require a filter but in reality it is far better for the fish to have a cycled filter on a tank for them. In a tank smaller than 5 gallons (with 1 betta) it is conceivable to keep a betta with no filter (still requires a heater) but with daily 50%+ water changes(depending on size). To try to keep more than 1 betta in a tank of that size without a filter....is poisoning the fish. Even if you are doing a 100% water change daily, there is just too many fish in that tank to keep it sufficiently clean.
I highly suggest getting a tank of AT LEAST 15 gallons if you want to keep your bettas in a divided tank like you have them set up now. That way each individual betta will have at least 2 gallons and room to move. You will need a heater that is sufficient to heat all the sections to a good temperature and good filtration for these tanks to work. You also need to look into how your fish are getting into the other's sections as this will always be an issue with divided tanks. I have kept plenty of divided tanks, ranging in size from 5 gallons to 20 gallons(all with divided domestic betta splendens).
