That book has misinformed 20+ years worth of students unfortunate enough to have a prof dumb enough to present it as anything more than a long political tract. Basically, everyone the US opposed was ackshoolee the good guys, but aw shucks, they always lose. Really it is just plain anti-American, there is a point you cross when it's just obvious you despise your own country.
And yes, absolutely Zinn was a commie. After he died, the FBI put out his file:
Zinn's File
It's hundreds of pages. When it first came out, I read the whole thing (the old school FBI files make for interesting reading, from what they release, most of these people had good reason to be looked at). Here he is in 1949 (so way earlier than some others) protesting in favor of some commie sponsored Jewish thing:
View attachment 2679606