"To this end" or "To that end"
In this sentence, end does not mean side, it means goal. To this end means In order to achieve this goal.
Whether you say in order to achieve this goal or in order to achieve that goal makes very little difference, if any.
If your sentence was to win, he has to run to this / that end of the trail, there is a difference, with this, he has to start from the far side and come towards the speaker, whereas with that he runs away from the speaker to the far end of the trail.