In American law, the word "highway" is sometimes used to denote any public way used for travel, whether major highway, freeway, turnpike, street, lane, alley, pathway, dirt track, footpaths, and trails, and navigable waterways. This road matches a few of those descriptives. Vaguely.
In practical and useful meaning, a "highway" is a major and significant, well-constructed road that is capable of carrying reasonably-heavy to extremely-heavy traffic.
I suspect either the State Sign Shop didn't have a sign that read "Bi-way", the Sign Shop Crew needs better supervision, or more likely, for the goat trail to be eligible for a certain charitable Babe Ruth of Pork Barrel's Federal funding, it was labeled a "highway".
Roadway terminology clarification, politics and speculation, along with the thrilling adventures of Lucky the Duck, all here on Panhandle Ping Pong