Wrong. Biden has never run in the general election for the office of president. He ran for the democrat nomination for president.
He was on two winning tickets in that regard.
Well in one sense you are correct. Since he was running in the democrat primaries there was no real election occurring.
The democrat primaries are a series of dog and pony shows that have no effect on the nomination. The DNC completely ignores the results, if the results are actually tallied at all, then selects who they want to win. They could save a lot of money and news coverage by cancelling the faux primaries and just announce who they selected.