Gatherer is correct; the ability of a
Winding Constrictor entering the battlefield in this situation will not apply to the Constrictor itself, and therefore
Winding Constrictor should only receive one counter.
To see why, let's dive into 614.12 a bit; I've bolded and colored the important bits:
614.12. Some replacement effects modify how a permanent enters the battlefield. (See rules 614.1c–d.) Such effects may come from the permanent itself if they affect only that permanent (as opposed to a general subset of permanents that includes it). They may also come from other sources. To determine which replacement effects apply and how they apply, check the characteristics of the permanent as it would exist on the battlefield, taking into account replacement effects that have already modified how it enters the battlefield (see rule 616.1), continuous effects from the permanent’s own static abilities that would apply to it once it’s on the battlefield, and continuous effects that already exist and would apply to the permanent.
So in this bolded section, 614.12 is explicitly defining the set of replacement effects that modify how a permanent enters the battlefield, and it does so by listing two basic classes of such replacements: Replacements from that permanent that affect only that permanent (
Colored red), and replacements from sources other than that permanent. (
Colored blue).
The rest of 614.12 is then a bunch of further detail about how to determine which replacements from within these basic classes should be applied, but none of that detail matters here, because we already know enough to know that
Winding Constrictor's ability should not be applied, because it does not fall into either of these basic classes. It doesn't fall into
the red class, because it affects a general subset of permanents, and it cannot fall into
the blue class, because its source is the Constrictor itself. Therefore, it does not apply.