Reaction to stimuli doesn't mean sentience. A computer reacts to stimuli, plants react to stimuli, and even baking soda reacts to stimuli with vinegar.
But like you said, how (i.e. motile vs not motile) a being reacts to stimuli can be a teller.
We're able to know all those parts are required for sentience because of the role they play, and all those roles are required to achieve sentience.
We know that to have subjective experiences (qualia), certain steps are needed after information about the environment is gathered - or the information would just be that, information with nothing else to it.
We are able to determine they are not only responsible for sentience, but required for sentience, because of the steps that would be needed to achieve sentience biologically (explained in the quote), and because those parts fill in those steps that are required to arrive at 'qualia' being possible.
It's easier to understand with the letter example written in the page:
All those parts coming together will make a being be aware of his surroundings and be able to experience subjectively (interpretation).To understand this more clearly, a comparison can be made with delivering a letter, where the letter is an information that can be interpreted subjectively:
1- Without the somatosensory system, there is no letter. The delivery person (thalamus) carries nothing, and the receiver (your awareness) receives nothing.
2- Without the thalamus, there is no delivery person. The letter is there, and you're ready to receive it, but nothing happens.
3- Without the thalamocortical radiations, you can't grab the letter from the delivery person and open it, nor can you and the delivery person see each-other. The letter exists, and it's ready to be delivered, but it's not able to be grabbed and opened.
4- Without the cortex, you don't know how to read the letter. The letter exists, it's delivered, and it's opened, but it's unreadable.
In all the cases, you won't know what the letter has to say (can't be aware/sentient).
And yes, of course, you can test and verify this with every organism you can find. Without these steps, no organism is sentient. No organism is able to feel and experience subjectively - and their behavior confirms it.
While when all those steps are there, there's at least a basic form of sentience (like insects).
There are different ways to test if a being is sentient: Turing test, prolonged observation to see how it behaves and if it shows signs that would mean sentience (like showing fear by cowering and running away, and learning to actively avoid what was causing fear), seeing if it's limited to classical conditioning or has operant conditioning, etc.
Once you understand that a being is sentient, you can examine how it's possible, and compare it to non-sentient beings to see the difference.
And the difference is a central nervous system, which is at the very least made up by the parts written above (in some cases, the mid brain functions as the cortex for a more primitive brain).
As soon as a being is able to gather information, and transmit it to the central nervous system (brain) to be interpreted subjectively, sentience is possible. But a brain is required to have qualia, otherwise there is nothing that can process the information in a way that would make the being be able to interpret it himself.
The more these parts get complex, the more complex experiences you can have (and therefore more intense, more nuanced and unique, etc.).