How to support 1 corner of stair landing
Yep, doing another pair of sticks under the landing where the chimney used to be is quite enough. Slip a galvanized plate under the existing &amp; new leg to prevent moisture wicking. With your new sticks, anchor the first stick to the cinder block, even with just Molly or Mushroom Head Bolts before attaching the other stick.

This will avoid any possible future racking or pull-away type movements. Not that it would, but you can also avoid the anchors by doing an X-brace of sticks between the then 2 supporting legs or posts, so you don't make any holes in the walls.