No, if no one claims a draw, it can continue forever.
In perfect play either black or white resigns in their first move or agrees to a draw.
But in in-perfect play you could get a situation where it plays until heat death. You at the very least could wait for a bit flip on the memory of the opposing player that might let you win.
Of course two Kings can't checkmate each other. If the board bit flipped, well that would be cheating / not a proper game. So in this specific case it'd be agreeed to a draw without the 50 move/repetition rule by the most basic of programs since checkmate is not possible given any play. But legally they wouldn't have to, unlike the above scenario when it can make logical sense to continue.
In perfect play either black or white resigns in their first move or agrees to a draw.
But in in-perfect play you could get a situation where it plays until heat death. You at the very least could wait for a bit flip on the memory of the opposing player that might let you win.
Of course two Kings can't checkmate each other. If the board bit flipped, well that would be cheating / not a proper game. So in this specific case it'd be agreeed to a draw without the 50 move/repetition rule by the most basic of programs since checkmate is not possible given any play. But legally they wouldn't have to, unlike the above scenario when it can make logical sense to continue.