I think you're reading too much into it - Cleric PCs draw their mechanics from the domain they choose, not the deity that grants them access to that domain.
For the purpose of the playtest, it doesn't matter whether you get access to the "Fire" domain because you worship Asmodeus, or Lathander, or Hestia, or Imix, or Surtr, or just the abstract concept of the sun - it matters whether the "Fire" domain is functioning properly as designed or needs some tweaks. It'd be a different matter if the Asmodeus "Fire" domain and the Lathander "Fire" domain were mechanically distinct and needed to be tested independently, but at that point each deity would effectively be its own subclass, or even multiple subclasses.
Talking about the deities that exist in the multiverse that the PCs can choose from has a purpose for developing the character's mindset, motivations, backstory, etc., but I wouldn't expect them to devote too much page space to them in the playtest, any more than I would expect the section on wizard school subclasses to deep dive on the Red Wizards of Thay.
That's a topic for the final book, not the playtest docs.