I see your problem. You are confused over the meaning of hominid.
Apparently, the folks at wikipedia are confused over the meaning of the term hominid, since I didn’t make that quote up out of my own imagination.
A little further research shows that the people putting out the New World Encyclopedia (which I think you quoted) put the dillema thusly:
“A hominid is any member of the primate family Hominidae. Recent classification schemes for the apes place extinct and extant humans, chimpanzees, gorillas, and orangutans in Hominidae, and thus technically hominid refers to members of these groups. However, historically and even in some current classification schemes, Hominidae is restricted to humans and their close, extinct relatives—those more similar to humans than to the (other) great apes, which were placed in another family.”
and more detail is provided later in the article:
“For many years, humans were placed in the primate family Hominidae, and considered hominids, while chimpanzees, gorillas, and orangutans were placed in the primate family Pongidae, and labeled as pongids. Over time, particularly since the 1960s, the use of morphological and genetic studies led to the recategorization of primates and the placement of humans, chimpanzees, gorillas, and orangutans together in Hominidae. In such a scheme, the use of the term hominid would properly refer to all four groups, and their extinct relatives, and thus hominid is being used more commonly in that sense. Indeed, the terms hominid and “great ape” are now effectively interchangeable among many zoologists.”
So, it seems even your own source admits the current trend among scientists is to classify existing great apes (and I would assume extinct great apes) as hominids.