Fix chess example

[thongonary]

Why are these changes needed?

The nested chat example for tool use in conversational chess has a few incorrect minor details, which are confusing to people.

• In the illustration, the Player Black Agent chooses make_move(c3c5) but then the board proxy agent moves pawn from e2 to e4.
  
• In chess, white always moves first. The example lets black moves first, but then in the board's illustration, it's white's move.
  

This PR fixes both of these issues:

• Fix the illustration to make sure the moves are consistent
  
• Switch the initiate_chat roles so that Player White makes the first move, consistent with chess rule.
  

Related issue number

N/A

Checks

• I've included any doc changes needed for https://microsoft.github.io/autogen/. See https://microsoft.github.io/autogen/docs/Contribute#documentation to build and test documentation locally.
• I've added tests (if relevant) corresponding to the changes introduced in this PR.
• I've made sure all auto checks have passed.

[ekzhu]

@thongonary thanks for spotting!