This sentence does not make sense. It would need to be How many kinds of computer networks are there?
"The computer network" in this sentence implies that there is a singular network that somehow has plural types. If this is not what the sentence means the definite article is unnecessary and, actually, wrong.
Drop "the" to make the sentence correct in English. "How many kinds of computer network are there?
Why does the ng in mạng sound more like a glottal stop?
I think because of the hard downward tone. I've noticed in the north, it tends to be harder, and often seem to include almost a glottal stop.