Not the same situation as having a Pope and a “Pope Emeritus”
Aside from the title “Pope Emeritus”, the situation was exactly as it is now, and was recorded that way in the history books. Celestine V resigned by his own design and a conclave began on 23 December 1294, ten days after his resignation. Benedetto Caetani was elected in his place as pope, taking the name Boniface VIII. Celestine V attempted to retire to his old life of solitude and was an ex-Pope for 2 years during Pope Boniface VIII’s papacy, where he was attended by two monks of his order, until he died at the age of 81 in 1296.
If Francis is an illegitimate Pope because Benedict is still alive, then so was Boniface VIII.