A game on Steam called Retro City Rampage has a protagonist that looks (loosely) similar to "Claude". He has the black jacket and signature black Elvis styling hair. He has more blue than green pants.
Weirdly GTA 2 has similar game style (top down and most of it set into some sort of future) but the future is from the viewing of years ago as the DeLoreon time machine is included.
The game starts with a heist that goes wrong (like GTA 3) but then the person escapes in a time machine which sends him to an alternate universe similar to GTA 2 when the heist was set in a place much more like GTA 3 so that game maybe a hint to the early GTA's as this is what it was inspired by.
This means that Claude MAY have been transported to somewhere in the future by Zaibatsu. As it is Liberty City in 3, Anywhere city/Anywhere maybe a future version of Liberty City from a Retro-Future aspect.
Most of the vehicles have a retro-futuristic look as well as the above.
Here is a pic of the protagonist from RCR.