According to the paper you referenced, from the Bureau of Labor Statistics, in private industries and under the category "Management, professional, and related occupations" employees earned more actually – $35.70/h – compared to workers represented by unions, who earned an average of $32.95/h.
I would assume the majority of software engineers work in private industries, thus would fall under the aforementioned category, and as a result would actually earn more by not joining a union. Am I missing something here?
Furthermore, it's unclear whether those wages include other types of compensation, such as stock grants and bonuses for example, in which case the difference would be even greater.