He happened to lose his case -- but that doesn't mean due process was denied to him.
In fact, that is why he lost his case. He did not lose his case because the First Amendment did not apply to him.
You have recognized that there were two issues in the case. The second issue was whether due process was denied. The court found that due process had not been denied.
The first issue was whether or not the "due process" clause was even applicable. The court "assumed" that the First Amendment was among the "liberties" protected from deprivation of due process by the states. If the court had not made this "assumption", then there would have been no protection regarding due process.
"Due process" played no part whatever in deciding the first part of the case. The Supreme Court noted that the First Amendment, which only specifies that "Congress shall make no law", applies to the states.
Now, where did the Supreme Court come up with the idea that the liberty of free speech which is protected in the First Amendment is a liberty which the states must recognize? This case is notable because, prior to this case, the First Amendment did not create an obligation on the part of the various states to protect that liberty.
The Court was able to make this decision because the Fourteenth Amendment has more clauses than just the "due process" clause. All issues of "due process" were decided against Gitlow. The only decision that the Supreme Court made which was notable was that the First Amendment limits state action.
That is what is called "incorporation". It was an invented term to describe the glacially slow pace with which the Supreme Court deals with the applicability of the Bill of Rights to the states. Such applicability arises due to the "P&I" clause of the Fourteenth Amendment.
The First Amendment provides "immunity" of the citizens of the United States. That is the reason that it was mentioned in the Gitlow case. Issues solely of "due process" would not have required consideration of the First Amendment.