The process of impeachment is covered in this answer. As reported there, President Ford once said that 'high crimes and misdemeanors' are:
whatever a majority of the House of Representatives considers it to be at a given moment in history.
That quote gives us enough framework to evaluate the question. I'll take each reason for impeachment in turn (treason, bribery, other high crimes and misdemeanors).
At some level, this is a legal question. I am not a lawyer, so I'll defer to some legal experts.
The law faculty at the University of Missouri has a page on impeachment which discusses the history of how the framers set this part of the Constitution. Before adoption, the term used was 'maladministration'. At the time of adoption, it was changed to 'high crimes and misdemeanors'.
It does seem that the framers' intent may have been that this level of buffoonery would be impeachable. That is only important if you think that the opinion of the writers of the Constitution is important.
On the other hand, there is an argument to be made that this only covers willful maladministration. The examples provided in the debate (also in the linked article) are all examples of where a ruler chooses to abuse their power for their own benefit.
However, a large part of the question is also political. That part is flexible. In practice, a President could be impeached for anything that Congress impeaches them for. The Constitution is often less a set of formal rules for how our government acts, and much more a set of transient guidelines which are open to change.