Unearthed Arcana is a compendium of optional variants and ideas, and they generally are not as fully-detailed as the regular rules are. In particular, we have fairly little to go on here: Unearthed Arcana does not describe precisely what “feature (as some class)” really means, and what relationship the variant class has to the some class that the feature derives from.
In fact, the closest Unearthed Arcana comes to discussing this situation is actually discussing something of an opposite: what happens if someone multiclasses between two variants of the same class, and thus gets duplicate features. The answer to that is
Identical class features should stack if gained from multiple versions of the same class (except for spellcasting, which is always separate).
Unfortunately, this leaves us in an ambiguous situation where you could argue for or against this working.
The argument in favor:
So you could argue that since your ranger wild shape is “as druid,” then ranger is kind of a “version” of druid, at least for the sake of wild shape, and thus would stack per the above quote.
The argument against:
The opposite argument is to say that no, Unearthed Arcana is talking only about druid/druid multiclasses here, and so this rule has no bearing. If that is the case, then the ranger/druid has two copies of the wild shape feature as described in the druid class description, and that makes zero mention of the possibility of getting it twice and having it stack—so it doesn’t. Contrast with, say, the uncanny dodge feature, which says
If a character already has uncanny dodge from a second class, the character automatically gains improved uncanny dodge instead, and the levels from the classes that grant uncanny dodge stack to determine the minimum level a rogue must be to flank the character.
Since wild shape doesn’t have that, the argument goes, this doesn’t work.
In the end, we really can’t do any better than pose these two arguments, and say you should ask your DM which holds here. For what it’s worth, I have routinely allowed players stack class features gained through variants (or just from later classes that also had these features), and it’s been fine. I can’t recall any druid/rangers, but that doesn’t give me any especial pause here. After all, druid is (by far) the more powerful class, so even if your wild shape is stacking, multiclassing to ranger will weaken you relative to a single-classed druid, so I have no concerns this will be overpowered.