Green Lantern has a bit of a troubled history, since the book basically fell into the sales gutter by the late 60's, as Marvel sales skyrocketed and books like GL and Flash couldn't continue selling on their name alone like Superman and Batman. GL got hit the absolute hardest, and though some good stuff was done in the mean time, it's not really remembered to this day.
They tried a major relaunch in the early 90's, but it also flopped.
Finally they just completely scrapped everything and started over with Kyle Rayner, which gave GL a big shot in the arm, but it was at the expense of all of the lore GL had built up before, and eventually sales went back into the trash can again over the years.
So Johns' GL was the first time GL had been a huge success; Johns basically tore down everything that been done with the character since the 70's, brought back the Corps, brought back Hal and his supporting cast, reimagined his villains, and set about expanding his universe. This was at a time where DC was regaining traction in the market with an increased focus on bringing back old characters and continuity, having more crossover events, more violent and dramatic storylines, and GL was one of the headliners of all this, especially after Sinestro Corps War was the biggest summer event they'd had in years and promised a shit ton of new stuff in the future.
So yeah, the no-kill stuff was a holdover from the late 60's and early 70's where DC had a lot of rules against characters killing even as the Comics Code started to become more lax. One of the consequences of rolling everything back to that era is you got all the more "dated" elements like that.
You really should start back at the beginning of the run, or start with Green Lantern: Secret Origin. SCW builds on all that stuff.