However, I don't understand how the brain activity patterns can prove (or disprove) that women and men have 100% equal ability to do math. I just don't see the connection between those two things.
A clear disproof or proof would involve observing a hard constraint of some sort.
For a blatantly counterfactual analogy imagine that they found neural patterns for math were literally the same as computer processors done in brain cells like bored engineers implementating computers in Dwarf Fortress or Minecraft. They could decode patterns and found human calculations involve bit registers in their head - men fit between 3 to 6 base five "bits" directly and women have 2 to 5 base six "bits" as size constraints prevent fitting more in. They found larger numbers were done via piecemeal operations over a memory map slowing things down and increased clockspeed was possible but would literally cook their brain. The upper bound for men in this bizzare hypothetical world would be higher.
Anyone could have guessed this, because it's common sense. But the purpose of science is to produce knowledge based on empirical evidence. Common sense has its place, but science wants to test everything. According to a scientist it's not a fact just because it's common sense. Now this fact is part of the body of scientific evidence, and that is a powerful thing.
If you are trying to figure out why men are so inclined to math/CS, I think it makes a lot of sense to start at the very bottom of the problem; what do their brains look like when they are literally doing the thing? We can officially rule that out, so now we can fairly move up the chain and introduce more complex questions.
This study didn't find any such difference, in the study both gender's brains worked in the same way. They studied children in an attempt to factor out some other influences (i.e. societal).