And I can't help wondering how. Yes, I know the answer will be 'magic'. But what could their child look like? Moreover, it's unclear whether the Minotaur is unique, but the Sphinx certainly is. She was designed and created to serve one purpose -- guard the tomb. Why would her creator give her ability to reproduce? First, there aren't, and should never be, any other, including male, sphinxes. Second, if she somehow managed to successfully mate with something else (as apparently is the case), the result would be a number of half-sphinx-half-something creatures with totally unpredictable looks, moods and behaviours. As a software developer (albeit novice) I have to say that this feature was both totally useless, extremely unwise and potentially very, very dangerous (I doubt that her offsprings would also be obliged to guard the tomb). And I presume that there exist no 'wands of create sphinx', and therefore her creator should be quite an intelligent person, intelligent enough to foresee the possible outcomes.
According to TV Tropes, I go on and on when it comes to this subject, but I feel I ought to address the issue here.
You are making a few assumptions about various species in a fantasy world. Specifically, that certain creatures were "created" and are not species in their own right.
I put it to you that the Sphynx (as I have come to deliberately misspell it), is a *summoned* guardian creature rather than a *created* one. My resource for this one is the old 2nd Edition AD&D gamebooks where the Sphinxes clearly belong to a set of 'races' that have a wild, natural state as well as being occasionally summoned to guard duty.
They are broken into a few subraces:
The one that appears in YAFGC is a Gynosphynx. A lion body with eagle wings and a woman's chest and head. The male counterpart to the Gynosphynx is the Androsphynx. Andros have more leonine manes and heads with human faces. Andros are more inclined to violence while Gynos are more intelligent and fascinated with riddles and puzzles. There are also Criosphynxes, which are goat-headed sphynxes and Hieracosphynxes which have eagle heads. These two appear to be species of their own, but can also mate with Gynosphynxes. Producing what, I'm not sure. Presumably either more of their own kind or Gynosphynxes.
In the real world these kinds of pairings are either impossible or, rarely, produce sterile hybrids. But this is magic and fantasy. Science is optional and usually intrusive.
The minotaur of Greek Mythology is a unique being. A cursed man who was once normal looking and got the head of a bull. "The Bull of Minos" lived in a labyrinth and was miserable. In YAFGC (as in AD&D) the Minotaurs are a race with males, females, a tribal community, etc. I'm not sure if I ever outright made that clear in YAFGC but there are things that will come out in the future that will. Turg has a mother, father and brothers who are also Minotaurs.
How can a Minotaur and a Sphynx reproduce??? Well, as I showed in the strip at the end of the "Reflections in the Sand" story, they have access to polymorph magic and have been taking turns being both Sphynxes or both Minotaurs (and possibly other things). According to the "Guide to Unlawful Carnal Knowledge" (an unofficial fan-compiled set of AD&D sex-related source material), this magic can allow creatures to procreate. AS THE SPECIES THEY WERE SHAPED AS WHEN MATING. So, one presumes, that if I were to strictily adhere to the book, when those Sphynx eggs hatch, the babies will be Sphynxes.
I did draw some MinoSphynx babies for a reader at the last Hal Con, but I am still undecided about how their children will appear.
As for the Chimera: Summoned or created? Well, he says he was summoned and the Dragons call him the eternal guardian. He's been around a long time, or at least, they believe he's not going away any time soon. And we do see a female one. I'm not one who will generally toss away details like that lightly. Again, according the the old AD&D resources, Chimerae are a species, though perhaps created magically originally, they do breed and exist in 'the wild'.
For myself I haven't yet explored that particular detail of his origin story and have some things still undecided. But it's clear to me that while Chimera isn't entirely unique they are rare enough that even HE doesn't know if there are others. It could be that others have made Chimerae and at least one of them is female for some reason. Female and with the head order reversed. Maybe she's the bride of the monster, made specifically for him? Maybe. We'll see. Someday.