The larger than life, almost comic book characters of the past just seem laughable in this day and age, with few exceptions, which is why most wrestlers these days have actual names rather than gimmick names.
Sadly, as you say, unless you are overly familiar with the current WWE, then it doesnt translate as well to the video game genre.

I think you only have to look at some of the gimmick names that have cropped up in recent years to see that gimmicks for the most part, dont work anymore.
The Boogieman, for example, probably would have worked 10 to 20 years ago, despite his lack of talent, but in todays day and age it was never seen as scary, just comedic.

As for the Legends of wrestling game, I bought that years ago, and it was just plain awful, bought it, played it for a day or two then took it back to the shop and swapped it as the shop was doing a no questions asked refund policy if you brought a game back within a week.

Of course there is the new WWE Legends of Wrestlemania game, but I dont believe thats on the PS2, and quite frankly when I played the demo, I was unimpressed.
While it uses the same engine as SD vs Raw, the controls are different, and I really did not like them.