Squire Dylon's goal was quite simple; to exploit his superior raw power to the absolute maximum in order to win as quickly as possible. He knew he was on a time limit, especially since attempting an offense in grappling was much more energy-consuming than attacking via striking.
Squire Kyrie's goal was also equally simple, to stall the fight for as long as possible and drain Squire Dylon's stamina as much as possible. She knew she had a stamina edge, once her opponent was exhausted, she could begin her offense and win due to a lack of sufficient energy from her opponent. She had an edge in grappling defense since Dylon was largely offensive as a Martial Artist, so she was confident that she could hold on.
The wrangled for quite some time, even spending a lot of time just immobile. Some of the Martial Apprentices grew a bit bored, since the fight had become less exciting than it had been prior. But Rui only grew more and more engrossed.