On my iPod I can manually move my songs around that are in my playlist, but I can't do the same on my phone which is what I mostly use. It would be easier to have that option on all devices.
In the update from Spotify in this thread they said:
"An upcoming version of Android will see this feature initially released to a small number of users."
So it's likely they're enabling the functionality via a feature toggle for a select range of users. In other words, the functionality is now contained in the current production release but isn't enabled for everyone yet.
This would also confirm why some people were able to see the feature after installing certain Beta releases but not others.
It's a common approach. Allows devs to test features in prod environment and gather feedback/usage data and tweak if needed before rolling out to all users.
Looks like Edit Playlist function first appeared in one of the betas a few weeks ago. Once a feature reaches production (albeit currently limited to small group of users) it probably means it's a couple of weeks away from full roll out (barring any major issues).
Spotify will likely not confirm operational specifics but I'm pretty sure that's how it'll play out.
