The diagram from Astronomy magazine is correct; the book excerpt is a little confused.
Winter solstice is not when the Sun appears opposite certain stars, but when the Sun appears farthest from the Earth's north pole.
The time-dependent difference between these is due to axial precession.
There are several different definitions of a year:
The book is incorrect. The calendar is designed to keep track of the seasons. What will happen in 13000 years is that the Northern Hemisphere summer solstice will still occur near the end of June, but it will occur near perihelion rather than near aphelion. In 13000 years, summers in the Northern Hemisphere will be short but intense, and winters will be both ...