Some companies are skipping résumés (or so we are told), saying the staid requirement doesn't provide much depth about a job candidates.
Old habits die hard, and resumés will likely survive for some time to come.
The issue is always how to stand out from the crowd. A good resumé will jump off the pile, and making a top effort is still important. Other vehicles are becoming more useful (and maybe important) but I think it depends on the industry and job category. Whatever gets you noticed is useful, and that might be a small web site, a blog etc. The issue is ALWAYS telling the reader how you can help them solve their problems. HR people and hiring managers have no interest in what you did - except that it can potentially be applied to their situation and help them make some money. My usual advice to those who ask is to write for your specific audience - and that is the decision maker in the hiring process. Make all your material (in whatever format) a solution to someone else's problems.
So, should you abandon your resumé? Probably not. Like the Chinese diplomat said about the French revolution - "too soon to tell".