How chess players play each other at every level? (6-3-5)

I believe the answer is:

across-the-board

I'm a little stuck... Click here to teach me more about this clue!

'at every level?' is the definition.
(everywhere or at every level)

I don't understand the remainder of the clue.

(Other definitions for across-the-board that I've seen before include "General" , "How men may move" , "generally" .)

I've seen this clue in The Telegraph.

Want a hint initially instead of a full solution? Install my app