Interesting.
But no need to worry, it's just sensationalism.
• First of all, the speed of Earth's orbit is between 66,650 mph and 67,150 mph. No real 666 there.
• Second, the curvature of the Earth is measured in linear miles, not in square miles. Square miles are used for area. This curvature is 8 inches per mile, which happens to be two-thirds of a foot, or about 0.666667 feet. This fraction is irrelevant, since there are 5,280 feet in a mile. The two units (inches and miles) are not on the same scale.
• Third, the axis is currently tilted at about 23.43 degrees. If you measure this angle incorrectly, by subtracting from 90 degrees instead of starting at zero, you could get 66.57 degrees. So, the WRONG measurement is close to 66.6, but it is constantly changing. Earth's axial tilt actually oscillates between 22.1 and 24.5 degrees over a roughly 41,000 year cycle. As the angle decreases, the Earth warms. We were in an ice age around 25,000 years ago and the Earth will continue to warm for the about the next 15,000 years, no matter what we do.
From there, these numbers get more and more ridiculous. 6x3=18. So what. And 2/3 is close to 0.666. But only close. Anywhere you find two-thirds, you can INCORRECTLY round it to 0.666. Two-thirds is actually 0.66666..... continually. It is correctly rounded to 0.67, 0.667, 0.6667, etc., depending on significant digits.
So, no need to worry about THESE claims, as interesting as they may be.
"Vicarius Filii Dei", on the other hand....