[Chess] Separate Chess specific attributes

[sotetsuk]

#1127

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 80.77%. Comparing base (e4c305f) to head (1d269a8).
Report is 2 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1226   +/-   ##
=======================================
  Coverage   80.76%   80.77%           
=======================================
  Files          61       61           
  Lines        5989     5992    +3     
=======================================
+ Hits         4837     4840    +3     
  Misses       1152     1152           

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