Hi,
First, a couple of comments. A tug-of-war is an event. You might call it a sport, but some people would say it is not organized and popular enough to be called a real sport.
The adjective from 'sport' is 'sports', eg a sports event.
I've tried to change your sentences into something that sounds like a natural thing to say.
(a) A tug of war is a sport and exciting game. A tug of war is exciting.
(b) The tug of war is an event on Sports Day.
(c) There was a tug-of-war on the sports event. There was a tug-of-war event on Sports Day.
(d) The tug-of-war is a sports event.
What happened to item (e)?![Smile [:)]](/emoticons/emotion-1.gif)
(f) We have tug-of-war in event of the sport. We havea tug-of-war as a sports event.
Best wishes, Clive