After launching RE, my firewall told me that an application named abbeycore_win32 is trying to get to the internet, and recommended that I block it - which I did. The game doesn't appear to be affected by me blocking said application.

So far, so good - or bad. How comes that this game is trying to do something with the internet without telling me, not mentioning explaining what's going on? Without my firewall I wouldn't have noticed that this is happening.
It may be that this has to do with the "community" stuff which is enabled by default, and which I can disable in the settings menu. Be this as it may, it is bad style, to say the least, to misuse customer PC's in this way, and I will definitely not buy anything else from these guys unless they fix the issue.
Don't get me wrong: I don't mind games capable of communicating with the internet - but I do mind games doing this without telling me, without asking me for approval.

If it's the community settings indeed: How about disabling them by default, and leave it to the customers to enable the feature, if they want it? I don't want to have it forced on me.

I would appreciate an explanation from the developers what this application is doing, what data it transfers from my PC where, and why they don't tell me that it is happening. Until this is clarified, I assume that Renowned Explorers contains spyware.

And finally, GOG would be well advised, in my mind, to protect its customers from such game behaviours.

The way I understood this issue is exactly as you think: the internet connection is for the data send to Abbey Games. Abbeycore is simply the game process which is run.

Regarding the not telling you: After starting the game, please look at the bottom right corner. There should be a message telling you exactly this: So:
1.) They are telling you they are logging data and they are telling it to you right at the main screen. Even earlier isn't really possible, is it? I mean the game engine just tells the firewall: "Hey I would like permission to access the internet" at the start.
2.) They are telling you how to disable it
3.) The default off would have been nice, but since it (hopefully) only sends data after you play, you can safely disable it right at the beginning and not bother with it
4.) ... or like you did, block it with a firewall and the game still works, unlike some other games which "require" the internet connection. ...

First of all, thanks for your reply. I didn't expect to receive any after such a long time (and not even the developers have bothered to say anything - arrogance or ignorance or silent acceptance of my points?).

To be honest, I can't remember having seen a message in the bottom right corner. Possibly I didn't even get that far when the firewall message popped up, and my blocking the internet connection for the RE application may have prevented the message from being displayed later.
By the way, I have un- and reinstalled RE today. There was no firewall message, and there was no message on the main screen talking about connectivity. Again, thinking positively, the reason may be that the firewall block wasn't removed when I uninstalled RE.
But the re-installation DID reset the settings of RE, and the new default settings fit with what I remember from my original installation: All internet settings (leaderboards, "community features", which include the transmission of my play data to an unknown server, etc) were ENABLED, and had I not bothered to check the settings before starting a game, I'm not sure what would have happened - it may be (and I assume this to be the case unless someone manages to convince me otherwise) that data would have been transferred back to whoever had I not disabled these settings.

So my personal experience with RE remains unchanged: RE is trying to collect information from my PC without telling me. I can disable this "feature", but neither the setting itself nor the method to disable it is apparent when I launch the game.
This fits my understanding of SPYWARE.

And finally, that you agree that it's not good that the default setting is "enable data transmission to whatever server" is nice, but it doesn't really change anything. I'm the customer, my data belong to me, and what would you think about someone doing business with you who says I'm going to take your property (to avoid the term "steal") unless you tell me explicitly not to? If such a behaviour doesn't violate laws (what it does in certain countries), it throws a telling light on these guys business ethics.
That this behaviour seems to be common practice today for many big and small internet portals, that they get away with it (for the time being), and that many people today don't seem to be interested in their property and aware of the value of their data, doesn't make this issue irrelevant or go away.

Sadly yes, the developers don't seem to be very active on the GoG Forums, but they are a very small team. That is strange. The only (positive) explanation I have is like you said: By blocking the game, it automatically detected that no connection could be established and it didn't show the message, since it wasn't necessary. (again: that's the positive way of thinking) You can check that in the Windows Firewall Settings. If you blocked it, then an entry should be somewhere in there. Since GoG doesn't have a cloud setting where your saves can be stored, the original settings are restored, that is correct. I would say nothing would have happened, since you blocked it with you're firewall. We would need to have the information of a developer here to answer this question thoroughly. Again: Yes in your case, no in my case ;) But it should be made even more clear (maybe just always display the message at the lower right corner regardless of the connection to the servers or not and simply also show the current settings: "Active" or "Inactive" and if a connection is currently established to the servers. That way you can't go wrong. I agree to 80% with you here. Normally I am also on your point, but in this case I lean to the side of the developers. They are telling it to me and how to disable it, so I am fine with the current setup (like in Minecraft, at least at the time I still played it). In your case it doesn't show you the message how to disable it and the whole thing turns into a potential data grabber with unknown size. I completely understand you from your point, I just want to tell you: the point looks different from my view, since I got the message on the screen. That still doesn't help you or your problem, but I just wanted to explain myself. I hope you still have many fun hours in the game, after you deactivated the settings and blocked it!

... Just an answer and clarification from a developer would be nice ...

Just checked: My firewall (Norton) didn't block RE - it does now. How this can happen, I don't know. There is the theoretical possibility of a Norton bug (or my own fault, which I find highly unlikely in this case), or RE changed the setting back when I re-installed RE (which Norton shouldn't allow without my approval). I'll not dig further into this issue.

I agree that I'm not REALLY worried about RE doing something terribly evil on my PC (Steam is definitely worse, but then these guys tell you in advance, and the user has to approve explicitly). But I don't like it, and I wanted to let the developers of RE know how I feel, and that they are losing at least one buyer - even when this is unlikely to impress them very much.