I think your own text explains it really.
-- a "chuckle" is more jovial overall (although there can be malevolent chuckles).
-- a "snigger" tends to be more on the meaner side in general.
That's why your text chose it to be in that order, IMHO.

Yeah, I already thought it to be like that but since I'm not a native speaker, I just wanted to make sure that I didn't made a mistake... Thank you anyway :D

Merry Xmas to you too! This may be different for BE speakers (chuckle vs. snigger).

I'm AE.

Schoolboys "snigger". Mostly at something they believe to be improper. I remember my biology teacher saying very early on to us 12-year-olds: "If you want to study biology, you have to stop sniggering every time I use the word 'sex'." To say that someone has sniggered implies that you think he's immature.

(A bit like "giggle" when talking of schoolgirls.)

Merry Christmas.

Is "snicker" simply an AE alternative for "snigger"? ("snicker" is (still) not used in the UK, AFAIK.)

Yes, "snicker" is AE, "snigger" is BE (AE).

"Chuckle", "snigger" and "giggle" are not yet full-on laughs.

-A chuckle is usually deeper (both in pitch and in site of origination) and born of good humor.
-A giggle is usually high pitched and may be born of humor or embarrassment. It is most often associated with girls and small children.
-A snigger/snicker is a repressed laugh, often accompanied by a repressed snort (sniggering is done through both mouth and nose), and born of "inappropriateness". Occasionally it is a synonym for giggle - teenage boys wouldn't be caught dead giggling; they snigger - though a snigger is usually lower in pitch than a giggle. The inappropriate element may be the emotion behind the snigger (e.g. malice) or the subject matter (e.g. the very word "sex" for 12-year olds) or the setting (e.g. not wanting to laugh at a funeral). As escoville notes, there is usually an association of immaturity to both giggle and snigger.

Just my take on the distinctions.