In accordance with both Jewish and Christian theology, there is only 1 God - Yahweh - who is the creator of everything: angels, people, animals, the universe, earth, etc. Worship of anything or anyone besides Yahweh was (and is) prohibited because only Yahweh has and deserves the rank of being divine. Keep these things in mind.
A demigod is, according to Google:
a being with partial or lesser divine status, such as a minor deity,
the offspring of a god and a mortal, or a mortal raised to divine
This idea of demigods exist in many mythologies, such as Greek mythology. However, this is not seen at all in the Bible. For the Nephilim to be considered demigods, they would have to be "the offspring of a god and a mortal." However, they are the offspring of the "sons of God" (which @SamBC said are angels according to ancient Hebrew sources) and of the "daughters of men." Angels are spiritual beings created directly by God; they are not deities, they are not divine, they are not even demigods. Thus, any offspring of theirs are not demigods.
To reiterate what @SamBC said, the Greek heroes and demigods were the focus of Greek mythology, and this is true to most mythologies. However, the Nephilim were not the focus of the story, let alone the focus of the Bible. They are only barely mentioned one other time in the book of Numbers.
Now here is an interesting idea. This passage could be the key to explaining (from a biblical worldview) many mythologies and legends. These Nephilim are described as being "the mighty men who were of old, the men of renown." Perhaps the demigods of, for example, Greek mythology were some of the Nephilim. Deuteronomy 32:17 calls false gods demons, using parallelism in the verse. Considering that the "sons of God" were angels who committed these perversions, they can be considered as fallen angels or demons. Perhaps these gods of mythologies are demons like these, and the demigods, their offspring, are the Nephilim.