Well we already knew that Trump isn't running to do the actual job of President, so this is no surprise...The most powerful VP in history, and he still turns Trump down. Now we know Trump is the REAL loser, not Kasich. Trump doesn't actually want to do the job of being President, he just wants people to call him "Mr. President", while he sits on twitter all day long.
The key sign of desperation when that offer was made is the implication of that offer. Donald Trump doesn't want to be President, he doesn't want a hand in domestic or foreign policy, he merely wishes to expand his brand and go down in the history books as the biggest showman. It was desperate and the implications are troubling.
Trump is delisional. He believes that he is always right and that he is the most beloved man on the plantet, especially among those he considers his peers. His appeal to Kasich was made out of that delusion, not out of any desperation or other lack of confidence in his ability.
Trump's offer to Kasich, to be "the most powerful vice president" in history, was not a sign of desperation. In fact, the offer never happened. This was simply a trial balloon. The best move Trump did not make was to have Kasich as his running mate. Kasich represents the very establishment that Trump is running against.