How should I reinforce this slide from my deck?
I would build a simple landing for the slide exit, either behind or in front of the exit face. The platform should be staked into the ground at multiple points to prevent shifting. By securing the slide exit most movement will be eliminated.
The problem with your mid-point post strategy is that it's difficult to make such a post laterally rigid. Ground is soft (even with a concrete base), and posts flex as well. You might end up with a rather unpleasant twitch rather than a gentle jiggle by eliminating just part of the movement. A better strategy would be to triangulate to the deck rim using rigid poles, but I just don't think it's necessary.