I think this is the locative noun, but I am not sure about the noun class and the meaning of this sentence (at home?, in home?, perhaps this is because "home" is Africa...)
nyumbani (adverbial locative noun in the pa, ku, or mu locative classes)
1) locative of nyumba
1) Second person plural:
you, (archaic) ye
2) With nouns, indicates location: in/inside, at, on
nyumbani (at home, in the house)
mezani (on the table)
"nyumba" just means "house", "nyumbani" means "home", hence here it is "nyumbani"
This seems more like "Tanzania is a home." You would need to add a possessive (e.g. "nymbani yangu") to say "Tanzania is home" since English implies "my home."
'Tanzania ni nyumbani' actually means 'Tanzania is my home' even if 'yangu' is missing from the Swahili version. The possessive 'my' in the swahili version is implied in this case