†1. Unbiassed [sic], impartial. Obs.
†2. Free from motives of personal interest; disinterested. Obs.
3. Unconcerned, indifferent. In this sense disinterested is increasingly common in informal use, though widely regarded as incorrect: see disinterested adj. 1.
1. Without interest or concern; not interested, unconcerned. (Often regarded as a loose use.)
2. Not influenced by interest; impartial, unbiased, unprejudiced; now always, Unbiased by personal interest; free from self-seeking. (Of persons, or their dispositions, actions, etc.)
So uninterested is indifferent (that is, the subject is of no interest or note). Disinterested may also mean that, but that would be to use the word loosely; less loosely it means unbiased.
From uninterested comes uninteresting — of no concern, not noteworthy, trivial.
Thus someone may be disinterested in a subject without it being uninteresting. It is not altogether correct to say "I am disinterested in that topic" means the same as "That topic is uninteresting."
The usage discussion in MW to which you refer makes much the same point. Since we have two words which have evolved to have distinct and useful meanings it is a shame to confuse them in loose usage.