Chinese person here, raised in a household that adheres to traditional folk beliefs - we generally treat 神 (shén) as gods in the sense that they're powerful beings that can be prayed to directly for something that falls within their sphere of oversight, rather than intermediaries (as mentioned by /u/3amthompson there are some, like the stove god Zaoshen/Zaojun, whose job is for example to report on a family's deeds, but we would still consider them to be 神 themselves). Many of them did start out as regular humans, but that doesn't disqualify them from also being deities. I'm not a theologian or anything, but the way I was taught about that was largely in the same terms that we talk about ancestor worship (in the sense that, following their passing as mortals, they continue to influence the material world and can be communicated with and beseeched for blessings through prayer and offerings).

I think one point of difficulty here may be the matter of different linguistic/cultural/religious ideas about what exactly a "god" is - the Abrahamic faiths have a very clear distinction between God, saints, etc., but this isn't necessarily the case in traditional Chinese faiths where things are somewhat more fluid. I wouldn't consider my late great grandfather to be a 神, but I make offerings at his grave in much the same way as I would at a shrine or temple of a local Chenghuang or Tudigong, and likewise when I ask for his protection I'm asking for it directly from him, not asking him to petition heaven for a blessing.

Another thing is the fact that folk belief isn't an organized faith in the way that, say, Christianity or Sikhism are, and it's highly syncretic - that means that it varies significantly from place to place and can incorporate elements of many belief systems. Typically, the main sources for that are Buddhism, Taoism, and Confucianism (which itself is debatably a religion, a philosophy, or something else entirely), but others are certainly possible; my own family's traditions mostly incorporate Buddhist and Confucian teachings, but we worship some Taoist deities as well. There's also some uncertainty about the extent to which such folk beliefs constitute a religion at all - my parents regularly make offerings at temples and keep a shrine in their home, but if asked I'm not sure they would call themselves religious. I believe the situation is similar in Japan with Shinto (which, incidentally, has kami (also written as 神) which I would consider somewhat analogous/comparable to shén).

While I don't know for sure, it sounds like the version of folk belief you learned about might have drawn partially on Abrahamic traditions? It certainly wouldn't be unheard of, and I don't doubt at all that some people do view 神 that way. However, my understanding is that it's relatively uncommon, and I would be cautious about generalizing that (or really any strict belief, given the diversity that exists under the umbrella) to Chinese folk belief as a whole as there are plenty of people who see things differently.