There's no contradiction between the 22nd Amendment and President Trump's position that he won the 2020 Presidential Election vote with the electorate. The 22nd Amendment states:
No person shall be elected to the office of the President more than twice
Furthermore, Article II Clause 3 stipulates how the votes for President should be counted and the President elected - and it doesn't mention the popular vote at all. Rather, it refers solely to the votes in the electoral college. President Trump does not deny that the electoral college voted to install President Biden - that was the whole point of his actions with regard to pressuring Vice President Pence not to certify the slate of electors on January 6th.
Trump's position is that despite him winning the 2020 election with the American public, due to voter fraud and vote rigging he was denied election to the presidency with the electorate that matters - the electoral college. Therefore, he was not elected to the office of the President more than once, and can run again in 2024 and be elected without being in conflict with the 22nd amendment.