That's probably not true, but set that aside for a minute.
Trump was impeached (this time) while he was President of the United States, so EVEN IF the "power of impeachment" granted to the House in Article I does not extend to private citizens, it would not apply here.
Impeachment is for office holders, to remove them from office.
Holding an impeachment trial on a private citizen is not constitutional.
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.
Since judgment "shall not extend further than to removal from office" and Trump is no longer in office, the impeachment becomes moot.
The Democrats want the second judgment (disqualification), but they must first obtain the first judgment, which is now moot. Removing someone who is already removed from office is like a double jeopardy, it's holding a trial after the judgment has already been rendered.
Pelosi and Schumer are just miffed that they won't get the chance to exercise the second penalty of impeachment because the Electoral College beat them to the first penalty.
-PJ