OK, see the part labeled 'F'? That'd be the bolt.
In a chain gun, there's a mechanical linkage between the chain and the bolt, so that the chain will be driven continuously, but the bolt will be cycled intermittently.

So, the chain doesn't actually feed rounds into the gun. It's just a more reliable way of cycling the bolt, as compared to gas-pistons or roller locking.

: But perhaps other folk developed the misunderstanding that
: 'chain' referred to a belt of bullets feeding into a gun, and thus the
: term was getting misused also outside of videogaming? I wonder if it got
: misused also in some action films or TV series for example.

Wouldn't surprise me; it's as big of a misnomer as believing that "RPGs" are a distinct class of anti-tank weapon. In reality, it's just a backronym for the Russian term for "Hand-held anti-tank grenade launcher".

: Dang, I seem to recall having the clip discussion before. Maybe even within
: the last two years or so. Just did a forum search too; nothin'. Maybe
: you'd care to remind me what a clip really is?

Nikko did a pretty good job of summing the difference up. I'd only add that en-block clips were implemented in more than just the M1 Garand, and were often an integral part of the rifle's internal magazine.

Oh, and what do you get when you cross an en-block clip with a revolver? Something magical.