I think Gene would be more than happy with the "new left". If you read Gene's thoughts on Star Trek's development you'll find social commentary was as much apart of it as Hornblower and Wagon Train. Wagon Train being one of the Adult Westerns he wished to emulate. Social commentary was part and parcel to the Adult Western sub genre. Gene's ideas evolved as the show progressed and so did the show's point of view and other peoples ideas (writers/producers/actors/) ideas were presented as well. So it wasn't just Gene shaping Star Trek.
Gene was a 60s liberal and embraced the hedonism and excesses of that time along with the progressive ideas. His blue print for Star Trek in the 80s followed those ideas even though the times had moved on and that era was more conservative, while Gene moved more left. (while never losing sight of the dollar sign.

) TNG from the get go was very much a "New Left" show. So I'm not sure I'd call him a classical liberal.
The article you linked seems to be an opinion piece. One person's interpretation of the relationship between Trek and Liberalism. For an article that show Gene's dissatisfaction with Trek in his latter years, it's woefully short on actual quotes by the man.