You're in great shape, because what you did so far got you employment for each industry as well as the total jobs in the industry. Now that you've grouped by zip_code and industry (you did that correctly), you need to follow up with a summarize(). Following the pipe chain you already have, try adding:
%>% summarize(percent_employment = sum(employment)/mean(total_jobs_zip)*100)
I can't check it without some kind of reprex, but I think all you're missing is the last step---summing employment across instances of "tech jobs" and then dividing by the total.