I still don't get it. Moving on

In fact the "game" is useless. You should have realized that it only serves to present numbers on a chessboard
with a funny property when you want to calculate their sum.
Hint:

1. Take a sheet of paper and a pencil
2. Draw a chessboard 8 x 8
3. Put the numbers of the description on this chessboard
4. Examine the numbers
5. Try to calculate their sum lazily and intelligently
6. If you don't see their particularities go to 4

When you have understood the problem for 8x8, add a row and a column, fill them with numbers following the same rules as for a 8x8 chessboard. Now you are ready for a nxn chessboard.
There are no spaces, no token to move around, the result depends heavily on n.
Have a good day.

PS: it's useless to say that a description makes no sense:-)

I updated it with some examples. I'll try to be more active on this site again :) sorry!

Do you need help?