In Hinduism, do we have any particular deities for sports and other activities for the players for praying before starting playing?
This is how wikipedia defines Sports. https://en.wikipedia.org/wiki/Sport
Sport includes all forms of competitive physical activity or games which, through casual or organised participation, aim to use, maintain or improve physical ability and skills while providing enjoyment to participants, and in some cases, entertainment for spectators.
So if the Aim is to improve physical ability and skills. Lets see which God is associated with physical ability and skills. Yes you are right He is Hanuman.
Kushti and Kabbadi are traditional sports in India, And where ever it was practiced and taught they have images for Hanuman.
Also Shiva is also very tall and powerful physically. He sits in the cold mountains, it needs enormous physical strength to do so.
As per Scriptures Hanuman is a avatar of shiva himself.
Hope this helps :)