"They say there were once gods other than elementals"
I agree, elementals - even Kossuth or the 4 Elemental Evil overlords - are not gods. But we see the end of a process. Much earlier (using the 4e book lore here) there were gods, which subsequently disappeared ... for some reason, unknown and lost to time. The worship previously oriented towards those gods was re-directed towards other beings of great power - elementals - which have subsequently been mis-identified as "gods" in the common understanding.
From what I can tell so far. The opinion that there used to be "gods" in Dark Sun seems to come from an unreliable narrator. And is probably untrue. (But if a particular table of gamers wants it to be true, they can choose to make it true, choosing a variant cosmological setting as an option.)
Animists lack hierarchy. (Aside from clan elders, who are still family.) Lack bureaucracy. Thus lack gods.
The assumption of "worship" is ethnocentric, mainly deriving from Hellenism. Albeit it can develop in certain cultures independently after establishing hierarchy and bureaucracy.
I suspect the familiarity with reallife Christianity that "worships Jesus" creates the false impression that all religions "worship". But this too is ethnocentric. Also it is shaped by Greek-speaking Hellenism. Even then there is an additional development of Northern European feudalism, where "worship" means to declare that someone is "worthy" to be the hierarchical superior. At some point (since the 1300s?) the related words came to increasingly specify the object of worship as gods or God. To be more inclusive of Non-Christian religions, it is necessary to be able to drop the word worship, and only use it when it is accurate and meaningful. The word "worship" is highly ethnocentric.
In Judaism, the word "worship" doesnt really exist. Albeit in Hebrew, we do have the concept of "serving" God (mainly in the sense of administrating the Temple), and perhaps more relevantly of "bowing down" to God as a hierarchical superior. Even then, literally bowing down forhead to ground tends to happen only once a year. For Judaism the sacred tradition is more about listening to God, thinking about what God says, and doing what God asks.
In any case, many reallife religious traditions have zero to do with "worship". Many reallife sacred customs are more like having a birthday party. It is sacred, and social expectations can be quite intense, and there can be very specific customs (seasonally honor a loved one, gather friends, birthday cake, blow out candles, sing Happy Birthday, give gifts, etcetera). But there is zero "worship" happening in these kinds of religious traditions.