Correct. The impeachment happened when Donald Trump was still in office, and therefore valid. The trial should now move ahead in accordance with the Constitution. A "conviction" (a 2/3rds vote of the senate as "Guilty") would remove him from office; he's already out because his term has Constitutionally expired, so that would have no immediate effect save for the second portion of the trial which determines, by a simple majority, whether to permanently bar Trump from holding Federal office again.
As it looks at the moment, the Senate is setting up to set a very unwise and dangerous precedent -- that of making it tacitly legal for a sitting president in the waning days of power to essentially have carte-blanche on his behaviour. The senate, in essence, will condone and further authorise future uprisings, riots, and mayhem at the hand of the president of the United States. Whither the rule of law? That's dangerous. Full stop.