Can you tell me what translation you're using? Greek frequently just writes ὁ θεός instead of naming a particular god. Like, more often than it actually names a god, especially in speech. The god in question might change, it might refer to no particular god. I mean, it's in the first line of the Iliad, μῆνιν ἄειδε θεὰ Πηληιάδεω Ἀχιλῆος, where θεὰ (not actually an Attic form, it's Ionic) refers to the muse, who is not explicitly named or called a muse. Super common in Greek, and a lot of older translators will simply translate it as God, rather than "the god"--sometimes, though, Greek will even leave off the article in that phrase, but it's not as common.

And no, the Olympians were hardly the only divine beings the Greeks understood. There were literally thousands of local spirits, which might take the form of nymphs and other nature spirits or hero cults--a major part of the Apology is establishing the precise divine nature of nymphs and satyrs with relation to the gods, but it's accepted by everybody at the trial that nymphs and satyrs are a sort of divine spirit, as is Socrates' δαιμόνιον. Apart from that there existed personal divinities (like Socrates' δαιμόνιον, but more generally various spirits of the house and family--in this category one might include the herms, which though displaying Hermes' image, might really be considered a separate thing), local cult versions of pan-Hellenic deities, supernatural powers to be placated or appeased, etc. In later times religious syncretism brought in (or wholly invented) a number of "eastern" gods, although this was already happening relatively early--Cybele, though never a major figure in the Greek world, was a Phrygian deity, and the (erroneous) tradition held that Dionysus was brought over from the east.