I have the exact same idea you do.
Until the GOG store appeared on the market, Retrogaming was seen as just a "curiosity" and retrogamers were mostly seen as folks who "liked to collect antiques". Of course, there was already "Retrogamer" magazine and a strong community on the web sharing and playing old videogames through emulators.
And let's not forget how important "Home of the Underdogs" was for making many folks rediscover the old PC classics (and even saving old PC games from oblivion).
But the gaming press and most gamers in general would never consider looking back at the old games.

The emergence of GOG and the fact that it managed to attract more and more customers proved that there was indeed a market for old games and solid money to be made from it.
Maybe I'm exaggerating its importance, but I think GOG indirectly played a very big part on the emergence of the "indie" game market, with games featuring "retro" aesthetics and pixel art. Many devs probably thought "if people want to buy old games, featuring old graphics, maybe they'll buy new games with similar graphics".

In the end I think GOG shot themselves on the foot, when they enforced their "curation" system, preventing many games from being sold in the store. And some of these games were likely influenced by the classics sold on the GOG store.

Maybe my analysis is wrong. Anyway... just my 2 cents.

Indeed, and many abandonware sites also .... they were booming with customers.

Heh, thanks. What do we know about Commander Keen not being here?

I honestly don't believe GOG had much of an influence. GOG is still not very well known after all these years (and I think it's only changed dramatically over the past few years, mainly due to TW3 and Galaxy & especially Galaxy 2), and it sure as hell wasn't well known when indie pixel art & retro games started showing up in ever increasing numbers a decade ago (or where ever exactly you want to draw that line). There are hugely influential titles (how about Minecraft?) that every kid on the planet knows...

I think it's more that the people who grew up with 90s NES/SNES/PC titles reached the age where they can actually pursue their dream of making games and put something out. It also happened to coincide with some popular tools that make game development much easier than it was 20 years ago. Now everyone and his dog knows how to make a pixel art game. If you were an indie game developer in 2003, chances are you were very technically inclined and at least reasonably interested in pursuing the ever-better compute capabilities of new hardware.

The other major factor was that publishing games got easier (e.g. Steam Greenlight 2012), and I suspect even Humble Bundles had a fair share of influence on the explosion of the indie scene which would also lead to more pixel art games getting made and seen.

I'm not so sure. Who was around selling Indie games on a big scale before Itch.io?

Itch.io

GOG have been around 12 years, and while they have been unknown for much of their early life by average gamers, they would have had some sizable impact on developers and publishers, and what goes around comes around. GOG would have shown you can work outside the major sellers etc.

I don't know if GOG can be said to be unknown by average gamers in their early years. When I joined in Feb 2010 there were already talks on gaming forums (specially abandonware ones) about a new store called GOG. In fact I came to GOG because someone mentioned it in a gaming thread.
I'll 100% agree with you concerning "hardcore" gamers, though. I think that crowd had few interest here and has zero interest in GOG still today (specially the MMO/Co-Op bunch.

And for plenty of years the gaming press gave GOG the "cold shoulder". I still remember how, whenever "Rock Paper Shotgun" announced the release of a new PC game, they only mentioned the steam store. And many people started to complain on the comments sections why the hell the site never announced the GOG release as well.
The same also applied to GOG sales and digital releases of previous unavailable old games. I think it was only after 2014 that RPS began announcing GOG releases and events.

Talking about old games such as WWII GI, I was reminded of the games The Wheel Of Time and the Carnivores series today.

Within the last couple of months, I was able to score one of the Carnivores games from Humble on sale, DRM-Free ... you got a download, plus a Steam Key. Carnivores: Dinosaur Hunter Reborn ... cost me around $10 or $11 AUD.

There are many Carnivores wishlists here at GOG, but only a few hundred votes at most, as of yet.

https://www.gog.com/wishlist/games#search=Carnivores

and

https://www.gog.com/wishlist/games#search=Wheel%20Of%20Time
You may be right, but I meant GOG in the context of an example, not really that of a seller of Indie games. Like I said, GOG showed you could go it alone and have some success, and not have to rely on being acceptable to a store like Steam etc. So until a major Indie supportive store like Itch.io came along, Indies were pretty much on their own in most cases ... the few exceptions aside. GOG would have contributed to their rise, if only in an encouragement sense.

When I first came across GOG, around 2008-2009, I alas still only had a 56K modem connection, and using the GOG store just wasn't feasible, even though it sounded great. I also wasn't all that sure how legit GOG were.

Because of that, I put them out of my mind, and because I hated Steam, I just focused on console games for my kids.

It was only many years later, due to a friend and my kids grown up, when I was thinking about getting back into gaming again, that I was pointed at GOG, for the free version of Shadow Warrior, a game I loved. That was May 2017, and the rest is history, with me having re-bought many of my boxed or cased games and many others since then.

So even if you were aware of GOG in its early days, you may have been put off for one or more reasons, as I was.