That, my friend, is a Libertarian.
No, "that" (I presume you mean GPM's/Jefferson's definition of a "classical liberal"), is a small-l libertarian, not a BIG-L Libertarian.
A small-l libertarian is very much like a conservative, but without the social-conservative (statist, big-government) desire to have their personal morality written into the Constitution.
A BIG-L Libertarian is a member of a political party with only tenuous connection to Jefferson's classical liberal libertarian. For the most part, BIG-L Libertarians are what give us small-l libertarians heartburn and a bad name.
No, my friend. It is not. I described a Conservative, not a Libertarian.