McConnell was not in charge of the Senate for the trial. The Democrats were. So there was a trial because the Democrats voted for it.
The Democrats have the majority in the House and Senate, however, it is the Constitution and the rules of the House and Senate that govern impeachment and trials. There was a trial because Democratic and Republican members in both the House and Senate followed the Constitution and the rules in both houses to impeach and proceed to trial.
McConnell is now just another Republican senator who can vote for guilt or for acquittal. He felt as others did that trying a civilian isn't constitutional. That only president can be impeached and tried for removal from office. Since Trump was already a civilian at the time of the trial, the trial is moot. So McConnell voted for acquittal.
The impeachment trial was clearly not moot. It was decided by a bipartisan majority to be constitutional which is why it proceeded. This was not the first time that the argument has been raised that a former office holder cannot be impeached and that argument has
never been sustained. Precedent supports the impeachment of former office holders as does common sense. The notion that the framers placed in the Constitution a provision for disqualification from ever holding public office again—due to egregious conduct
while holding public office—as a punishment for impeachment which can be avoided simply by resigning or losing an election is neither reasonable or logical on its face. The use of the word "civilian" is frivolous as
no one is impeachable for conduct that is unrelated to holding public office. However, anyone holding public office is impeachable and subject to trial for their actions while in office and that cannot be avoided by simply leaving office thru resignation or any other means. That said, a senator can use any reason they choose to justify their decision to convict or acquit regardless of precedent or rationality. The "jurisdiction to try former office holders is unconstitutional" argument is an artifice to provide a fig leaf of cover for acquittal. No doubt others will use the same excuse, despite the fact that the argument is superficial and defies both precedent and logic.