Many of the games on the alternatives list have exactly the same kind of violence.
If by 'the same kind of violence' you mean 'a different kind of violence'.
The NY times article refers to the ESRB rating. I'm pretty sure the article with the alternatives went by those. In your example the alternative, Overlord II, is rated Teen while its counterpart, Left 4 Dead 2, is rated Mature.
There are standards for these ratings. Now you may disagree with the standards, but dismemberment, animated blood and gore fall in the M category. Morality choices, like playing on the side of evil in Overlord, are not totally excluded from the standard, but usually have less impact.