" Your description seems to be based on what you see in the VI player. "
Yes. It was an example only, a hypothetical matrix on the simplest level requiring three keyswtiches.
"...I see what is clearly a list of articulation on the left...."
Not quite. It's a list of matrices. It's not necessarily choosing articulations. The selected matrix is in the middle, as you note, and the controllers that choose the performing cell within the matrix are on the right.
"...along the y-axis that appear to be mod-wheel settings, which are useless to me."
Here's an important distinction: the X and Y axis can be controlled by a lot of things. One of them is the mod wheel. This allows real-time (or recorded MIDI) to shape the performance on the fly. But you're looking for keyswitches, so when you see CC1, it's confusing you.
As a tutorial, do this: select the preset 73 Baritone Sax > SX-BR VSL Preset Level 2 ext.
Select the first matrix: C7 01 SX-Br Perf-Universal. You'll see a matrix with nine cells (3 x 3).
So where are the cell keyswitches you seek? There aren't any. ( Ignore AB-Switch for now.) That's because this matrix behaves according to the deft performance of the speed of your playing (X-Axis) and the movement of the mod wheel (Y-Axis). Stated simply, it's not designed to trigger sounds they way you want to trigger sounds. Note as well the shaded keyboard at the bottom -- just C7 to F7, which are matrix selections.
Now -- only as a tutorial -- click-hold the "Speed" drop-down in the X-Axis. Select Keyswitch. Now the X-Axis responds to your keyboard's C1 / C#1 / D1, and those keyswtches change the articulation. You can do the same thing with the Y-Axis, which will respond to C2 / C#2 / D2. See the keyboard again. Your new cell keyswitches are in blue and green.
"I just want to do something simple."
Indeed. Try this: from an empty VI, load matrix > Level 1 > L1 SX-Br Articulation Combi(nation). That's a 6 x 2 matrix. You could design an Articulation Set in Logic from C6 to F6 to get the general idea. ( There's only one matrix, so that doesn't need a keyawitch. And play with the mod wheel as a reminder that a lot of things can change the sound.)
Nothing is as complicated as it appears when we don't understand it. As an application programmer, you're going to breeze through this once things start clicking.