I've been an active chess player myself for a long time and for the last 8-10 years not just with the advance of engines but also online streaming there has been a lot of renewed interest. Saint Louis has become a big chess hub in the US, China has become a major player, Anand has rekindled interest in India, Carlsen in Europe and I would say today it is more popular than it has been in a long time, in particular in Asia.
As to the direct influence of engines the other innovations aside, it has definitely forced players at the very top to re-evaluate the chess metagame, find weaknesses in traditional openings and shook up strategies. For the strongest players engine evaluation has become a useful tool providing new insights. When people watch chess tournaments these days on the internet most websites will provide parallel engine suggestions and commentators use engines to take hints for their commentary.
In my opinion, engines have made the game more competitive at the pro-level and more accessible for casual viewers.