Resolves yes if a US President is elected before 01/01/2100 and isn't part of the Democratic party or the Grand Old Party at the beginning of his mandate. If the name of one of these two main parties changes, they still aren't comsidered third party.
How does this question deal with changes in the party system? In the 1852 election the two major parties were the Democrats and the Whigs. By the next election the Whig party was dead and the Democrats managed to defeat the new opposition, the Republicans, in spite of growing internal division.
A true "third" party win is all but impossible; it's a bit weird to count a realignment like that of the mid-1850s as a "third party win".
@BrunoParga if a new party is not considered a rebranding of one of the two current main parties, it will be considered a third party for the purposes of this question
@GastonKessler gotcha.
So this is essentially a question on whether the Dem-GOP party system will break.