Theory:

    “You understand that I am a Warrior?” said the stranger, feeling that perhaps this information had not penetrated Ranji’s head.

    “I have heard you say it three times,” replied Ranji.

    “Then why are you not running away?”

    “I am waiting for you to run away!”

    “I will have to beat you,” said the stranger, assuming a violent attitude, showing Ranji the palm of his hand.

    “I am waiting to see you do it,” said Ranji.

    “You will see me do it,” said the other boy.
Explanation:
 
Then the boy continued repeating that he was a Warrior, thinking that his statement hadn't reached Ranji's head or else he was not clear with what he meant. Later Ranji replied that he heard the strange boy saying that thrice. It implies that Ranji did not bother to stay away from him after hearing the strange boy said that he was a Warrior.

After hearing Ranji's response, the stranger asked him why he was not running away from him. Ranji said that he had been waiting for him to run away. After listening to Ranji's funny replies, the strange boy felt very angry. Then in an aggressive tone, the stranger, as he showed Ranji the palm of his hands, said he would beat him if he didn't leave the place. It showed the arrogance of the strange boy.

On the other hand, Ranji did not step back. Instead, he told him that he was waiting for that moment. The reason behind the statement was that Ranji was waiting for a fight to prove him as a Fighter. The other boy cautioned him that he would beat him, and soon Ranji was going to see that.
 
Meanings of the difficult words:
 
S.No
Words
Meanings
1 
PenetrateGo into or through something, especially with force or effort
2
Violent Using or involving force to hurt or attack
3
AttitudeA settled way of thinking or feeling about something
Reference:
National Council of Educational Research and Training (2008). It so happened. The Fight- Ruskin Bond (pp. 45-54). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.