"You all don't play with me"
Translation:Hamchezi na mimi
It must have been one of those odd answers that was reported so often that they corrected it some time in the last year. Now we no longer see the word that was being discussed.
But "nami" is indeed a contraction of "na" and "mimi" ("and me" or "with me").
Compare "nawe" from "na" + wewe" ("and you", "with you", or "you too"). http://africanlanguages.com/swahili/
Let's start from the positive form:
mnacheza = "you (plural) play".
m- is the subject prefix for "you (plural)".
(Occasionally they translate m- to "you all", to show that it addresses more than one person, but I would guess that the vast majority of English speakers use "you" for both singular and plural, and the majority of occurences of the subject prefix m- in this course are translated as "you". They just aren't consistent about it yet.)
-na- = present tense marker
-cheza = the verb "play". (It also means "dance" - take your pick.)
Now the present tense negative form:
- the negative marker ha- is added to m-
- the tense prefix -na- is dropped
- the -a at the end of the verb changes to -i.
So we get ha-m-chez-i = "you (plural) don't play" or "you (plural) are not playing".
and then na = "with" or "and"
and mimi = "me".