I think it depends on how you use the term "end times". A lot of people understand that to mean that the Antichrist is about to come to power, any day now.
From the prophecies of our Orthodox saints and elders, it sounds like we are in the general end times, when the end isn't too far away, could be a matter of decades, or a couple hundred years. But we're not in the very end, end times, when it's only a handful of years to Christ's Second Coming.
I suspect the fathers of St. Anthony's Monastery would believe that we are in the general, but not immediate, end times, because Elder Ephraim of Arizona talked about the Sleeping King.
Notice in the video that Elder Ephraim said that the Sleeping King will awaken and reign over the Orthodox, and that he will live 33 years. After his death, people will start to become decadent, and then the Antichrist will be born.
So the timeline is this: WWIII (very close now, maybe even this year, will be nuclear), then King Ioannis (30 - 40 years), then growing sinfulness (how long depends on the people of that time, surely at least a few decades, maybe more), then birth of Antichrist, then 30 years until he comes to power, then 3 1/2 years until the Second Coming of Christ.
I doubt any of us will still be alive when the Antichrist comes to power. Our children may be, or their children.
That is, if I've understood all this correctly.