Being the first to come up with an idea, being recognized as the face of the idea, and being the most influential proponent of the idea, are different things, and small details may decide which you end up as.
The fact that Schoenberg also wrote well-received late-romantic and atonal expressionist music before going dodecaphonic, that he was also a painter and a member of Der blaue Reiter, that he was well-connected in artistic circles in Vienna and held several teaching positions, that he wrote the influential music theory book "Harmonielehre", and that among his pupils were the likes of Berg and Webern, all add up to make him the more notable figure.
What's more, his version of dodecaphony, with the fixed order of the 12 notes in a row, sounds more radical (especially to the layman) than the tropes theory, and it is usually the more radical ideas which attract attention (both positive and negative, but scandal makes a person famous too).
The fact that he was and is better known makes him more influential, but that doesn't mean that Hauer's ideas were inferior, or that anyone considers them to be inferior. History just went in the other direction. Many modern discussions of Schoenberg mention that others were working on similar ideas around the same time, but we discuss Schoenberg because it was he who directly influenced many 20th century composers and music theorists.