Here is the relevant text: "The Senate shall have the sole Power to try all Impeachments. When sitting for that Purpose, they shall be on Oath or Affirmation. When the President of the United States is tried, the Chief Justice shall preside: And no Person shall be convicted without the Concurrence of two thirds of the Members present.
Judgment in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law."
The chief Justice of the Supreme would preside over the impeachment of a sitting president. It is true that Trump was impeached by the House while he was in office, but now he is out of office. Hence, the Chief Justice need not preside over the trial.
Article 2, section 4 " The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors."
So impeachment is not just for presidents.