The article says no such thing, and in fact doesn’t even address that issue.
The closest is the following: “It may not all be COVID on their death certificate, but deaths are up just huge, huge numbers.”
The person quoted isn’t commenting on hospitals at all. For example my uncle doesn’t have COVID on his death certificate but his doctor says that his case was simple enough that he could have been saved had he been able to be admitted.
True, but that statement doesn’t make the implication you claim; the other arm of the statement would have to be an assertion that the hospitalization rate would (or would not) have been higher had no vaccination been performed.
“Fortunately” (well for this argument anyway) there are natural experiments going on (including between US states, between counties in large states like California, and between European countries) that appear to demonstrate that vaccination does in fact reduce hospitalization
But reducing hospitalzitation alone isn't fair enough metric. What about people being disabled/dying from cardiovascular diseases as a consequence of mRNA therapy? They aren't taken into account by pharma and politicians. They are even going further against the common sense by blaming global warming!?