If the GM is 'intentionally' avoiding contacts from his/her customers either by asking his staff not to share his/her email address and/or ignoring correspondences directed to the GM (which it sounds like is what happened to the OP), then YES the GM has no clue on how to run a business in the hospitality industry.

It does not have to be listed on the website or put on noticeboards in the lobby etc. But if the guest requests to speak to the person in charge, the request should NOT be rejected.

Speaking of 'industries', do bear in mind that even in those where service standards is not as 'core' to the business as the hospitality industry, you are always given access to the person in charge upon request (electronics, law firms, restaurant chains, banks etc).