"The chair of the CMA, its chief executive and the rest of the board are appointed by the business secretary of the elected government" if I'm reading this correctly, UK citizens elect a government, the government appoints a business secretary, and then the business secretary appoints the entire CMA? So that would be two layers of disconnect from the voter.
AFAIK most US agencies are similarly disconnected or worse.
Whether "unelected" is a meaningful criticism to level at government systems is a separate question though. I feel like most roles are not ones where the voter could realistically have enough knowledge or education to actually make good decisions about who to appoint to roles with obscure or complex mandates. We seem to take democracy as an absolute good in all cases sometimes even though uninformed decisions can have catastrophic effects.
EDIT: I really shouldn't have to clarify this but apparently we're at the point where "this article poorly argues its thesis" is interpreted by some readers as "I love monopolies and/or activision"? So to be explicit: I think we need more antitrust enforcement, not less, but the article seems to make this case in a clumsy if not deceptive way