He acts like Plankton does in the mainstream continuity, but with differences. More notably, instead of attempting to hide himself from the others, he uses superior running speed and immense strength to allow him to try to get the Krabby Patty secret formula, since he is not small like Plankton.
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. The episode "Friend or Foe" can explain that a bit.
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 uses a rope to get in the Krusty Krab's kitchen and steal a Krabby Patty. SpongeBob then starts shooting clothes at Krabs until he is clothed in a bra. He then gives Plankton the stolen Patty and says that even if he didn't succeed this time that he'll keep coming back.
"Clothe me if you can, silly landlubbers!"
"Aw, ya got me! Well, at least it's underwire."
"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..."