It is often called Kokedera, which would be 'Moss Temple' in English.
Read more about Saiho-ji, the regulations for entering, and look at pictures of the green 'carpet' here.
Now for the stitch. I found Moss Stitch in A - Z of Embroidery Stitches 2. For those who have this book and can compare, you find that I have experimented with how to loop the thread, as you can see in my pictures below:
First make a cross stitch.
Twist the thread around your finger to make a loop :
Place the loop around the cross.
Insert the needle under the cross, but don't bite any of the fabric.
Pull the loop tight till you have a knot, and insert the needle below the cross to anchor.
You have made one Moss Stitch.
This is my 'Aida Moss Garden'!
As far as I know there is no Swedish name for this stitch.
Mattia, who always helps to find French names for the stitches, points to the French translation of Mary Thomas's Dictionary of Embroidery Stitches, where there is a stitch called Point de Croix Bouclé.
I had a look in my MTDoES in English. There is no stitch under the name Moss Stitch, but a similar looking stitch called Cross and Twist Stitch.
However, the knot is made differently.
Have a look:
The Cross and Twist Stitch is far easier to make! I wish I had seen it earlier! Thank you, Mattia, for pointing me in this direction!
Homework:1) You need to make a new Reference Chart as the first is filled with Stitches 1 - 42
2) On a red background make a moss garden with linen thread.