That same quote confuses me. If there are no events to measure time, why does that mean that time stopped? Can't it keep flowing just as space keeps expanding regardless of measurement? More so, photon decay is not completely ruled out yet, so events could keep happening in that cold photon bath.
It has to do with what time means. A coloiquial understanding of time has almost everything to with the way our mind and our memories work.
Our mind and memories won't be of much use at the end of the universe, so we have to depend on a more scientific definition. The best scientific way of describing and measuring time outside of our minds basically comes down to measuring systems as they increase entropy. As the universe ages, and these systems approach maximum entropy, the ability to measure time, and the ability to describe in any concrete way what time means, becomes increasingly difficult.
