This gets tiring repeating this over and over and still people don't get it.
They don't apply because:
There is no such thing as a "primary" for president.
There is only the vote by the Electors in mid December. Read your Constitution.
Here's what I mean by that.
The Constitution spells out the procedure for choosing the President and Vice-President.
Here's how it works:
The Electors from each state, all meet on the same day (that Congress chooses) and they write the names of two people on a piece of paper. One is their vote for President, the other for Vice-President.
At least one of the people voted for, cannot be a resident of the same state as the Elector.
Do you see anywhere in there, anything about a primary?
No. It isn't in there.
There is NO provision requiring any Elector to vote for any particular person other than at least one of their votes has to be for someone living in a different State than themselves.
There isn't even any reference to a list of candidates to choose from. They can write ANYONE down they wish.
State law, cannot trump the Constitution.
Thus, sore-loser laws do not, cannot, apply to presidential races.
Technically, EVERYONE is a candidate.
Now, here's why you are confused...
The Constitution says that the various State Legislatures shall decide how their State's Electors are chosen. In every State at present, the process is for voters to choose the Electors in a popular election, held at the same time as the Congressional election which is set by Congress.
In some states, voters cast votes for two Electors at large, and one from their Congressional district. In others, they vote for all of the Electors together as a slate. In still others, the Electors don't even appear on the ballot, but instead, the names of interested candidates for President and Vice-President appear. A vote for their choice for "President and Vice-President" is treated as a vote for a slate of Electors pledged in advance to cast votes for those people in mid December. However, do not be fooled by the last example. Even in that case, one is NOT voting for President or Vice-President. One is voting for the Electors. The office at stake is that of Elector, it is NOT President or Vice-President.
Thus the election in November is NOT an election for President or Vice-President, it is an election for the office of Elector.
Thus sore-loser laws do not apply.
Mr. Johnson will not be voted for in November. Electors pledged to him will be. Not a single vote counted in November will be for Mr. Johnson for President. All votes in November will be only for Electors. The Electors did not have a "primary" to participate in, the law is not triggered.
Mr. Johnson was never a candidate in a primary.
What we refer to (erroneously) as "Presidential Primaries" aren't really primaries at all.
Leaving aside the above explanation of the true process of electing the President, the event referred to as a "primary" for President is merely a partisan preference vote to indicate the preference of the members of a particular political party as to who they would like their party to nominate as an interested candidate for President later in the year at a party Convention.
You could lose a state's so-called "primary" and yet still be the party nominee and have your Electors appear on that state's ballot.
This proves that the so-called "primary" isn't really a primary at all.
In a true primary, if you lose - you are out. That's it. You lost. You CANNOT appear on the general election ballot, only the winners of the primaries can. (there are in this case, primaries for each of several parties)
Partisan primaries are a means for parties to nominate a candidate for the general election.
Another means is a convention or caucus of the party.
Another is a selection committee.
Not all states have partisan primaries.
The purpose of sore-loser laws, is because those states have separate qualifying dates and procedures for a candidate to qualify for the primary, and then for the general election.
In other states, there is only ONE qualifying period and procedure for the election as a whole. There is no need to re-qualify after a primary. Winning a primary is considered automatic qualification for the general election.
Thus to prevent the case of where someone seeks an office by becoming a party's nominee via a partisan primary from then later qualifying in the general election under a different party label, those states with separate qualifying dates and procedures passed "sore-loser" laws.
They could have also fixed this by making one qualifying date instead.
But in no case is any so-called "presidential primary" actually the determinate of who appears on a later ballot.
For example, Mitt Romney did not win the South Carolina "primary." But if he were to become the GOP nominee, his Electors will most certainly appear on the ballot in South Carolina in November. (but even if those Electors win, they are still free to vote for Newt Gingrich or anyone else for President)
It would be absurd for South Carolina to prohibit Ron Paul or Gary Johnson from having their Electors appear on the November ballot under the Libertarian or other party name because they lost the South Carolina "primary" while at the same time allowing Mitt Romney's Electors to appear, when ALL THREE of these men "lost" the South Carolina "primary."
Does it make sense now?
If Gary Johnson has a lawyer with even half a brain, he will win this case and his Electors will be on the ballot.