They are saying since 1880 because that's when they started keeping an official record

“This July was not just warmer than any previous July – it was the warmest month in our record, which goes back to 1880,” said GISS Director Gavin Schmidt.

That seems like an incomplete thought.

What kind of cycle are you suggesting, and why does the fact of "there's a second-place for hottest 30 days long ago" indicate a cyclic or repeating pattern?

I might wake today with a 24-hour temperature average that is hotter than any other 24-hour period except that one time I was sick as a child... but that doesn't indicate it's somehow normal or not due to events within my control.