Here's my question:
since it is a remastered version of Chaos engine,
does that mean that is can be played online as well, or it still only had local multiplayer?
(since I still own the original game, this would be the only real selling point for me.)

There is no online option, pure coop for two players with keyboard/joystick.

I'd also like to see some clarification on this issue. The trailer mentions "online co-op through Steam," so I am wondering if the GOG version also features online play.

No the gog version only has local wich is strange it is that i rather support gog but the gog version is more expensive and no online?

I guess the online features are made through Steamworks and are dependant on it, thus having been left out of the GOG version?

Damn. Pure damn.

I got it in those flash sales, counting with multiplayer co-op and turns out that the gog.com version is a "cut" version from the original? Not even LAN coop?

I will have to re-learn to not buy things on the rush, god dammit.