The thief's role in combat as a damage dealer is clearly exemplified by the backstab/sneak attack ability.
I disagree a bit on this.
The 1E/2E thief rarely got backstab damage in due to the facing rules. It was really difficult to get in behind a foe unless the thief was invisible, in darkness, or something similar. Backstab is even called out in 1E as a secondary ability. A thief was all about locks, traps, listening at doors, and hiding. Not damage. And thieves did not have the best to hit tables, fighters did.
3E upped the frequency of extra damage by allowing sneak attack if the foe was flanked or lost Dex bonus, but again, not the best chance to hit.
4E upped the frequency again with combat advantage due to how many effects (including flank) resulted in combat advantage (including allowing combat advantage in the very first round against some foes by a rogue) and equalized the chance to hit.
And 5E is even easier since both advantage and having an adjacent (not necessarily flanked) ally. This greatly improves ranged sneak attacks as well.
In each edition, the chances of backstab/sneak attack damage occurring in combat increased.
As to the amount of damage, it was upwards of 5x damage in 1E/2E, 3E was +1D6 per two levels max +10D6, 4E max +5D6 (but synergies from powers and feats blew this out of the water), and then 5E went back up to 3E levels of damage, but most of the 4E synergies disappeared.
So a Rogue was a striker in 4E because he did considerably more damage than non-strikers and had better chances to hit than in any earlier edition (and often had a better to hit than even other 4E PCs with feats and an at will designed for that). Previous to 4E, he wasn't really that much of a damage dealer. Even in 3E. Yeah, he could do some damage, but often not as much a fighter with an additional attack per round that had a 25% better chance to hit and more feats that could boost damage (bonus damage, extra attacks, etc.).
In 5E, the rogue is at best on par with a fighter (except maybe a Champion since those are weak sauce) because 5E fighters do so much more damage than 1E to 4E fighters. Although it's easier for a 5E rogue to do more damage than 1E to 3E rogues, he doesn't really shine as a damage dealer (compared to fighters or rangers) as much as he used to (granted, the 4E ranger outshined most PCs at damage). The 5E rogue is more of a damage dealer than some other martial PCs, but even there, he usually only outshines them at real high levels due to spell and special abilities synergies (e.g. compared to a Ranger: Hunter's Mark and Extra Attack and Colossus Slayer and Whirlwind attack, etc.).
Fighters and Rangers and even Paladins can do as much or more damage than a Rogue in 5E, that he cannot be considered a major damage dealer per se. Doing decent (but not necessarily great) damage is only one of the things he brings to the table in combat. Others things like uncanny dodge, disengage, evasion, etc. and hence not needing to be healed as much is nearly as important. Even the assassin is not that great of a damage dealer compared to some of the other martial types until level 17 and then at most once per encounter.
So, the 4E rogue was a major nova damage dealer, but the other editions, not as much, at least not until higher levels.