The actual text would seem to be: "Require an active license from the State of California and involve the practice of one of the following recognized professions: law, dentistry, architecture, engineering, or accounting." http://leginfo.legislature.ca.gov/faces/billTextClient.xhtml...
So, presumably no. Only engineers with a P.E. license (which has been pretty much phased out for software engineering).
Colloquially, we use profession to mean "I get paid for this thing." Traditionally, there are requirements for something to be a profession. A central licensing body must assert a professional has gained the requisite knowledge to practice. (The Bar serves this purpose for lawyers.)
The examples given imply this classical meaning of "profession". As you've pointed out, engineering in this context means jobs you'd need a license for, like civil engineering.
So, presumably no. Only engineers with a P.E. license (which has been pretty much phased out for software engineering).