[Chess] Extract game logic functions

[sotetsuk]

#1127

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 80.63%. Comparing base (5c5e74e) to head (c87444f).
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1227      +/-   ##
==========================================
+ Coverage   80.61%   80.63%   +0.01%     
==========================================
  Files          61       61              
  Lines        5944     5949       +5     
==========================================
+ Hits         4792     4797       +5     
  Misses       1152     1152              

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