When his mainstream counterpart and Mr. Plankton's mainstream counterpart were arguing about their burger formula, a new universe was created/was diverged. Instead of Plankton abandoning the project, Krabs did. Krabs opened the Chum Bucket and stopped wearing clothes possibly because of insanity or he couldn't afford them. The episode Friend or Foe can explain that a little. He started trying to steal the Krabby Patty formula from Mr. Plankton, similar to it being the other way around in the mainstream continuity. When the mainstream Plankton took over this universe's Plankton's job, Krabs confused that Plankton to be his Plankton. He used a rope to get in the KK's kitchen and steal a Krabby Patty. SpongeBob then started shooting clothes at Krabs until he was clothed in a bra. He then gave Plankton the stolen Patty and said that even if he didn't succeed this time that he'll keep coming back.
He acts like Plankton does in the mainstream continuity, but with diffrences. He probably stopped wearing clothes due to insanity or he could not buy them. It appears that he doesn't even like to wear clothes.
"Clothe me if you can, silly landlubbers!"
"Aw, ya got me!"
"Enjoy your victory screech, Plankton, because someday the Krabby Patty formula will be mine!"
(From the phone) "And the next day...and the next day...and the next day..."