Our city just went with IRC, we used to be UBC.
You may want to check with your local B.D. for code as the IRC (2003) says 7-3/4" max. riser height and UBC 8" max. riser.
Minimum tread depth - IRC.... 10" UBC .... 9"
The weak points in your stringers are at the V point of the landing notch. The downward pressure (load) is concentrated on the middle area of the level cut on the landing. Picture the tread/riser broken off with the wood grain, and the notched area splitting at the v notch. You'll be left with a 4" piece (rip) of material carrying the center treads. Your set is small, I wouldn't worry. If you had a longer set, I always level cut the waste piece overhanging the landing (air wood) the thickness of a 2x6, or two. Add them to give total support.
Actually, I plan for full bearing of all stringers on the landing return. Your landing would extend another 6" into the closet space. And I always add 2x4's as stated, for a finish stair skirt board, next to drywall. If wallboard only, I add 3/4" material instead. (for wallboard, don't have to stair-step the cuts) Some would make you fix or replace this if not to code, when you go to sell the place. Be safe, G