Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother in Islam, we are very pleased for the great confidence you repose in us and we really commend your apparent interest in having a better understanding of the teachings of Islam and the rulings of this great religion in all matters. In fact, Islam is a religion that encompasses all aspects of life and secures guidance and light for all mankind.
As far as sports and games are concerned, Sheikh Faysal Mawlawi, the late deputy chairman of the European Council for Fatwa and Research, states:
A Muslim should shun all games and sports that contain rituals and practices which contravene the teachings of Islam, irrespective of their names or titles. If sports and games are free of such non-Islamic practices, a Muslim is permitted to involve in them.
It is a custom in some martial arts that players greet each other by bowing. Then, if this practice is meant to be an act of worship, it is impermissible for a Muslim to involve in.
However, if it is meant to be a form of showing mutual respect between players, and not in form of ruku` (bowing) in salah, then it is permitted from the Islamic point of view.
Allah almighty knows best.