In fact, the LP really an educational outreach institution that uses the form of a political party to carry it's message. The difference between this kind of organization and a real party is spelled out in a classic of political science, E.E. Schattschneider, Party Government, publised in 1942.

Schattsie explains how parties are an inevitable outgrowth of the organization of caucuses to coordinate concerted action in the very first Congress, which inevitably became just two caucuses, which inevitably expanded their efforts into elections, and inevitably remained just two due to our first-past-the-post single member district system by which we elect Congress and legislatures.

Schattsie's definition of party is an organization that seeks to gain control of the government and has a plausible chance of doing so. The plausibility generates excitement and support among a wider population, but the organization itself does not include that wider population any more than the Chicago Cubs organization includes all their fans.