Seems like you need to be signed in to play DOOM 1 & 2 in the DOOM Classics Collection PS4 physical. You will be unable to play the two games offline. : r/LimitedPrintGames
DOOM II PS4 Review - PlayStation Universe
Three Original DOOM Games Now Available on Switch, PS4, and Xbox One - OnlySP
DOOM 3 PS4 Review - PlayStation Universe
DOOM II (Classic)
DOOM II (Classic)
DOOM Classic PS4 Review - PlayStation Universe
DOOM: The Classics Collection | PlayStation 4 & Nintendo Switch - LGN