I find the whole "chess" referance kind of silly to be honest.
The reason being that especially with the older MK titles, the characters had a very specific set of moves that were universal between the characters. Punch, kick, sweep, uppercut, etc... with minimal differances between the characters except for their special moves which were reasonably well balanced.
This to me made MK more "chess like" as both players function using the same exact rules for the most part.
In comparison, Street Fighter has always been a game balance nightmare. While Mortal Kombat was never balanced, Street Fighter has always been extremely unbalanced. The characters in Street Fighter are more unique, but do adhere to something of a "tier" system, with some characters simply being outright better than others. Even arguements by fanboys about it being balanced tend to fall flat when you start looking beyond the moves themselves, but towards things like ease of execution compared to relative power.
I remember reading that when they were working on Guilty Gear, their design philsophy was oddly one of ignoring any conception of game balance, and making every character as broken as possible, hoping that it would more or less even out, and they could balance it later. It worked to an extent, but one of the reasons why I think they moved on to "Blazblue" (which is not without it's problems) was that they were running out of things they could do to help with what was a fundementally broken product.
I'm not getting into whether Street Fighter, or Mortal Kombat is more fun. What's more nowadays I think they are both on a fairly even level of broken game balance, and tier arguements. Showing why I don't think fighting games in their current state will ever become a major form of mainstream competition. I just think Mortal Kombat has in the past come far closer to being a "Chess like" experience where everything comes purely down to the player.
Of course arguably, we saw a "chess like" approach to the genere beore either Street Fighter or Mortal Kombat, in the form of things like "Karate Champ" where both of the characters were identical in their move sets. I think it's possible to get to a "chess-like" competitive level without resorting tot hat with fighting games, but it's a case where balance has to be put before everything, rather than just being given lip service.
Then again I'm one of the people who has argued that they should add about 3 extra nessicary motions to the "Shoto" fireball of Streetfighter and other ranged attacks. The moves are fine, but are far too easy to spam rapidly given the results that can be achieved by even a relatively unpracticed player in doing so.