Until a good name is found for a genre and sticks, the similar games are usually called clones. GTA and Doom weren't the first in their respective genres (Wolfenstein even codified the foundation that Doom would expand on.), but were the most popular.
Anyway, I thought the term "GTA clone" finally faded away, like Doom clone. Now, don't we call them open world, or wide open sandbox, games? Tack "crime themed" to the front of one of those terms for games really similar to Grand Theft Auto's theme.
I am getting a kick out of how he complains about people comparing Jak 2 to GTA, when Jak's mission hub, and many of the missions themselves, are blatantly lifted from GTA's design philosophy. (Naughty Dog always seems to make their games based off of what is hot on the market.) Though, he has a point with Spiderman 2. IGN, y u no use brain thing?