Are functional resume formats acceptable?

No - recruiters overwhelmingly prefer reverse chronological (most recent job first) over the functional format, which groups skills and achievements together from all your jobs under common headings. Here are a few reasons why.

First of all, it's not so much about what you do (duties and responsibilities in a job), it's about the scope of that particular position and the achievements you had while in that role. In the case of a store manager, the recruiter doesn't want to read about how you were responsible for sales, customer service, staffing, etc. - they know that already - but they do want to know details about your particular store and what you accomplished there. A functional resume doesn't work because the details of each store you managed and the achievements you had in each location will be different.

Remember, recruiters want to see your career path. They are not just interested in what you've achieved over the course of your career, they want to see when you achieved it, who you worked for when you achieved it, what position you were in when you achieved it, and the scope of that position at that time. That's very hard to do using the functional format, and it makes for a challenging reading experience for the recruiter because it likely means they have to scroll up and down your resume to piece it all together.

Functional resumes have also historically been viewed with a certain level of suspicion. Recruiters have seen job-seekers use functional resumes to try and hide gaps in employment, demotions or other positions that veered from their career path, and other things that may be more obvious in a chronological format. That's built up an inherent lack of trust over time.

To make the best possible impression on the recruiter, stick to reverse chronological and let them see your true career path and the impact you had on each store.

Hope that helps. Cheers!