Steam game libraries routinely become worth hundreds or thousands of dollars as you spend more money to acquire digital goods. You can't move those to a different account, sell the entire account safely, or activate the titles you already own on a new platform. Nobody would spend all that money on repurchasing all their games just because the EA launcher is more shiny.

The lock-in cost is real and literal. It's far easier to migrate to a different voice comms system (which is free, usually), since you only have to convince your existing social network to create an account on the new thing.

Why would users need to re-purchase everything just to adopt a different store launcher as their primary platform? GOG Galaxy for instance interfaces with most existing stores and friend networks. As long as you're buying games on PC, you're not really locked into much of anything.

That said, buying certain games can lock you into using Windows. So there's that. But it's far better than buying games on modern consoles, which force you to use some special-snowflake hardware just to access the game you bought.

It's impossible to completely prevent all classes of lock-in, but it can be minimized. I would argue that my personal lock-in is minimized, across the axes I care about, by buying everything from Steam and GOG. No hard Windows dependency, no silly hardware dependency, and I'll almost certainly still have access to my games in 40 years.

First mover is a strong part of Valve's position: they have almost two decades of not failing their users under their belt, very few other digital content purchase platforms have a similar backlog. iTMS appeared a little earlier, but the rebrandings haven't exactly been helpful in terms of perceived seniority and it didn't really start with a wide audience, because non-pirated access to hl2 was much less of a rarity than non-pirated filling of ipods.

And as long as Valve does not burn that trust (there have been a few hickups in the very first years, but quickly forgotten), their lead can only grow. You can't throw money at the problem of potential customers wondering what the chances are that the service will still be around in five years. I'd even say that throwing money would only increase doubt: the more money invested, the higher the threshold of success required to be considered worthwhile of continuing.

Wasn't battle.net the first mover? I think it's way older than Steam. But I am not sure now

It is older by a few years, but it is not a two-sided marketplace, it's Blizzard's (+ Activision's) DRM.

FWIW, I did not mean that Steam is necessarily the literal first game marketplace, but to my (limited) knowledge it was the first one that got large enough to become the "default" option.

but it wasn't a general marketplace for games.

To be fair Steam wasn't either, in the beginning, which also ruins my argument wrt the iTMS quite a bit: even the Orange Box was still a retail product to most (it's even in the name!) that just happened to be consumed through Steam. Not much different from how iPod users had to use the client app for CDs bought in retail (or far more likely: mp3 from the Napster substitute du jour)

You couldn't download even blizzard games through battle net until 2013. Steam's first third party games were in 2005. They're not really comparable.