How does it work exactly? If it gets enough votes it gets put in GOG? Or is something else at play too?

Lots of other things at play. :)
GOG (and publishers) just use it as a way to gauge interest, and (for GOG) to see which games to maybe prioritize going after, or maybe get ideas for titles they hadn't thought of. But there isn't really a hard "magic" number of votes necessary to add a game, nor a threshold below which they absolutely won't bother. If there are thousands of votes for a particular title, but the rights are locked away with someone unwilling to release here (at least, under terms with which GOG is comfortable), or GOG's tinker gnomes absolutely cannot get it to work acceptably on their in-house test computers, then no dice: away it will stay. And if another game has no more than a couple hundred votes, but GOG can get the distribution rights as part of a package deal from the current owner, and there are no major problems getting it running reliably, then they'll release it, safe in the knowledge that someone will have a nostalgiagasm over it, regardless of how mediocre (or objectively bad) it really is. :)

Is there a way to tell what games are coming to GOG? Or what games are coming down the pipeline to be added at some point ?

The community does a decent job at figuring out at least some of the upcoming games:
https://www.gog.com/forum/general/games_that_are_unofficially_confirmed_for_release_in_the_future_part_2

AFAIK, not a single game has been added to the GOG catalog based on votes.

And the entire voting thing is a joke, for instance, some wishes have been incorrectly marked completed, like when GOG has added a "remastered" version of some game, but marked votes for the original title completed.

And how would you Know that?

As GOG isn't open about their inclusion process, I wouldn't.
But we can still use some logic to deduce that.

If there haven't been any indie games that have had massive votes and then suddenly appeared on sale, that would indicate that at least there isn't a direct correlation there. As far as games like LucasArts classics or whatever go, I wouldn't count those, as their inclusion is more based on what Disney wants to do with them than any voting.

Steam does many things wrong, but Steam Greenlight was easy to understand, and (presumably) votes there actually had direct effect on games becoming accepted.

As you've said, GOG doesn't give details behind their decision to pursue or accept any specific game. Everything you stated is baseless assumption on your part -- and to make the sweeping statement "not a single game...", without any data points but your subjective inferences, is bizarre. If we're playing that game, I could say, "As far as I know, every single game has been added to the GOG catalogue based upon votes," and it would be just as true.
The "as far as I know" part is key: neither of us knows much beyond what GOG reps have stated publicly, but they have stated in the past that the wishlist has helped them bring some publishers/rights-holders around (I don't have a link to any such statement unfortunately, but I'm sure someone else can corroborate, if you doubt me). Of course that probably hasn't ever been the only factor convincing another entity to allow a given game or series to be released here -- but I never claimed it was, nor, as far as I'm aware, did GOG -- and it may not have often been the most influential one. But I don't see any reason to doubt that it has been helpful for them.

If we're going to rely on our own "logical" assumptions, I would guess that the wishlist has most often come in handy when they're trying to convince some "small-time" rights-holder of some older game or IP -- cases where it's just some random, non-video-game-related (maybe even non-entertainment-related) individual or company, who might not even be aware that there's any demand at all for old video games (or, at least, theirs). Big game publishers like EA are certainly driven a lot more by their perceived long-term corporate interests than by a few thousand votes on a virtual petition asking them to sell their game on a store that they perceive as less advantageous to them.

Opus Magnum was almost certainly added due to community demand. To be fair that wasn't just based on votes but a lot of forum complaining as well. But that's one example of a game that was added solely due to community demand since they had turned it down in curation originally.

Data points are in the votes and release dates.
It should be possible, although time-consuming, to go through all games released on GOG, to see their release dates on GOG, then go through votes for that game, if any exist, and see if there is any correlations between them.

I dare say there aren't any - at least none has ever been brought up in any discussions.

The first I have ever heard of is the Opus Magnum case mentioned in this thread, and whether it was accepted based on those 645 votes or not, I don't know. This tweet can be interpreted in many ways, but from a certain point of view, GOG does seem to acknowledge that they changed their minds because of reviews, not votes.
http://twitter.com/GOGcom/status/958717863875014658
But let's say that might be the possible single exception, but generally speaking, votes don't seem to make any difference at all.

The very idea of GOG wishlist is somewhat bizarre. GOG catalog is based on curated choices, which often don't seem to make much sense to an outsider, but they have some internal criteria for them.
If GOG wishlist actually does something, it would change the focus from curation to people's choice, and that obviously hasn't been the way GOG catalog has been managed. You know very well that isn't true.

When GOG first started, they brought in whatever games they managed, that was not based on any votes. I'm not sure if wishlist even existed in the beginning (can't remember that far back...).
When GOG grew and started to get more publishers, they added whatever games they could get from already signed publishers, if it was all wishlist based, there are some titles that wouldn't have made it to the catalog.
For instance, there aren't any wishlist entries for Simon the Sorcerer anniversary editions, and yet they were added to the catalog, and the original games were removed from the catalog.

It's also obvious that GOG doesn't seem to care much about what the wishlist entries actually mean.
If you browse through most voted games ever, there are titles such as Full Throttle (24 682 votes), The Secret of Monkey Island (20 002 votes), and Day of the Tentacle (18 342 votes). All of these entries have been marked as completed, although none of those games are actually on GOG.

Yes, there are remakes, but not the original games which these entries are referring to. This is extremely easy to verify, as for instance, many comments for Full Throttle date further back than when the remastered version was even announced.