I'm familiar with the basics: case, gender, declensions, etc.
The above sentence refers to one of two males, if that helps.
My understanding (might be wrong): - "One of them laughed" so "One" is the subject, i.e. Nominative. "Ein von ihnen" just sounds wrong to my ears, but I don't know why.
Isn't the nominative of male nouns simply "ein"?
Update: Thanks to Hubert. It seems I was not as familiar with the basics as I thought. Here is some info on indefinite article declension (which I just went and read up on myself) for anyone else seeking it: https://deutsch.lingolia.com/en/grammar/pronouns/indefinite-pronouns