Not quite... alexithymia is being unable to put words to feelings. It's in the word... a- is not, lex- is words, thymia is feeling. Lacking words for emotions is not the same as not feeling the emotions.
Alexithymia is a common experience, but especially common when other communication barriers exist.
That may be the etymology of the word, but the article describes it differently:
People who do have alexithymia may describe themselves as having difficulties with expressing emotions that are deemed socially appropriate, such as happiness on a joyous occasion. Others may have trouble identifying their emotions.
Such individuals don’t necessarily have apathy. They instead may not have as strong of emotions as their peers, and may have difficulties feeling empathy.
That's affective alexithymia you're describing, but it's not the only mind. Cognitive alexithymia is closer to what this person was describing. A lot of the time it's not necessarily just one or the other, it can be different degrees of both