Sorry, but I don't think there exists such a game for Linux. However, if we're talking about any game that can be played on Linux, then you have to install scummvm and maybe dosbox too.
For scummvm you can try really any of the games, many have good plots. My personal favorite is Full Throttle ... now this game is not free, you would have to buy it (if you can find it) ...
So most of the lucasarts ones are good plot-wise, so are a few of the Revolution Software ones (Broken Sword), and other various ones, the ones I've played and are good:
Legend of Kyrandia *, I Have No Mouth, and I Must Scream, Flight of the Amazon Queen, Broken Sword 1 (the better one), Gobliiins (not much of a plot, but well made), Sam & Max (you must play it), Full Throttle (must play), and others.
If you can't play them well in scummvm for some reason, I've found some games to play better on dosbox.
Oh, and you can use the Exult engine to play the Ultima 7 that doesn't really work well on dosbox:
Also note that many of the games are abandonware ... not exactly legal ... but at your discretion ...