تُحْفَةُ الْمُؤْمِنِ الْمَوْتُ is a short but complete nominal statement. تُحْفَةُ الْمُؤْمِنِ identifies “the believer’s gift”; الْمَوْتُ tells us what that gift is.
الْمُؤْمِنِ has a genitive ending because it is the second noun of the possessive construction, whereas الْمَوْتُ is nominative as the predicate.
Ask two questions: “Whose gift?” — the believer’s. “What is the gift?” — death. This distinguishes possession from the subject–predicate relationship.