Mindfulness when playing chess
In contrast to the other answers, it is my perception that mindfulness and deep intellectual thinking complement each other.  

Sports are not about defeating the other team but rather raising your own performance to a higher level.  The higher level of physical or mental (chess) performance is a result of this alignment between the mind, body and spirit.  

As a skilled chess player, my best games come not from furious concentration but rather from an openness to the possibilities and patterns of the board. Indeed many chess players compare their state of mind to Zen or Taoist mindfulness.  As with a koan answer, the right move often comes as lightning.  

The mind can be trained to be present and creative at the same time. Both take a lot of practice however.  A novice chess player will be looking for the next move and confused by all the possibilities.  Just so, the novice meditation practitioner will be confused by all the stray thoughts.  

I'd encourage you to quiet your mind and emotions during a competitive chess game (not easy) perhaps the deeper possibilities on the board will be revealed.