If the only way a game has built in for multiplayer is connection to a central gaming service such as Gamespy or similar, then that's just not possible without modifying the game's source code or serious hacks to the game binaries which are unlikely to happen due to the expense of the engineering effort required per-game to do it for the projected payoff it would receive. It would have to be games where a bean counter could reasonably estimate an increase of revenue from the game if multiplayer support was enhanced or made to work again, and that the increase in revenue would be directly the result of the multiplayer modifications.

The only way to do something like this without modifying the game's own source code to enhance the multiplayer features built-in or binary hackiing it to do the same, would be to create an external binary that completely duplicates the functionality of the online gaming service that the game only knows how to communicate with, and hijacking DNS on the local computer to redirect queries from the game to the local fake service instead of Gamespy (or whatever), and then have the fake service code have a method for doing LAN broadcasts within itself to find or announce games over the local LAN to other games that are up with their own fake services running in the background. This would be a herculean effort, and the online gaming service backend server code would have to be reverse engineered for every single video game service and possibly every single game one at a time individually.

That's not something I can see being a financially viable investment of GOG.com's finite resources compared to many other things they could have their limited number of developers working on which would benefit everyone and the business much more.

As for VPNs, that does not help out the situation if a game does not support LAN mode or Direct IP mode already. A VPN would allow you to connect players over the Internet who are playing a game that no longer has working multiplayer servers but does already have built in LAN support. The VPN in this case forms a LAN virtually over the Internet so that all computers within the VPN are within the same broadcast segment. That works great using software like Hamachi, Tunngle, etc. GOG could create and provide such software if they wanted to but not without an investment of cash (which might not be worth it), however that would not help people play multiplayer games over the LAN that do not have LAN support already, just the opposite.

Likewise for DirectIP mode, if a game doesn't support that at all, there is no way to do it without modfiying the actual game itself because there is no user interface to type in the IP address or hostname built into the game, and the game on the receiving end is not programmed to receive an incoming connection request like that. It's not something easily hacked up in the middle with magic. :)

Adding multiplayer support modes to games that do not have it already is not as trivial as some people think it is by inserting a magic binary in the middle that fakes everything. The only "easy" thing that can be done is using a VPN to make existing LAN support in a game add private online multiplayer support to that game, but not the reverse.

All of the above only talks to the way everything works from a technical perspective, and the financial incentive (or lack thereof) to do the work though, it does not touch up on the legal side of things. If GOG were to add any kind of multiplayer support code to individual games or through some special software they create themselves to enhance the multiplayer aspects of any game or games in the catalogue, they would have to get permission from the publishers of individual games to allow them to do this either from a legal perspective and/or from the perspective of not trying to go behind a publisher's back to do things the publisher doesn't want. If GOG just did whatever they wanted and a publisher wasn't happy about them circumventing their intended multiplayer offerings - the publisher could just remove their game from the catalogue (probably all of their games), or try to sue perhaps for circumvention of protection mechanisms or possibly breaking laws regarding reverse engineering or something. In other words GOG ultimately would need to have a publishers blessing on anything they might consider doing because not having that would be a good way to piss off and scare away the publisher and possibly other publishers as well.

If GOG has the blessing of a publisher though, then they can possibly get the source code of the game and implement the needed functionality properly rather than with some ugly hack.

Just looking at this all from the perspective of technical, and legal reality, and the various incentives that would need to be present for such a thing to go from the world of "gamer community fantasy" world to "product feature target". I love the fantasy idea of course, but the technical/legal aspects and herculean efforts required for what IMHO would be very little ROI makes it unlikely in light of other projects the same resources could be spent on with much ROI for the manpower commitment.
That's like saying "What's the point of GOG Galaxy? We already have Steam Client." or even "What's the point of GOG.com, we already have store.steampowered.com" :) The point, would be for GOG to have features available which they create, provide, enhance and have control over as a customer service enhancement benefit of using the GOG platform and its services, and as a competitive advantage against other platforms that don't have such features, and as a "us too" to compete with other services that have similar offerings, and not have customers have to use a whole bunch of different 3rd party services scattered across the Internet to have their needs met by providing many of them all in one space with one login.

Also, competition is a good thing as is having your own service offerings and not being reliant on 3rd parties to provide services to your customers. 3rd parties have a funny way of being here one day and vanishing the next, possibly causing companies that rely on their services to have to scurry to find another solution (that may not exist). Gamespy anyone?

A GOG provided service or feature of comparable offering, blows away a 3rd party service and need for yet another login hands down anyday IMHO.