Device-independent quantum secret sharing (DI-QSS) provides security against untrusted quantum devices. While device-independent quantum key distribution (DI-QKD) using Mermin-Peres magic square game [Zhen et al., Phys. Rev. Lett, 2023] has been proposed, we present the first DI-QSS protocol based on a pseudo-telepathy parity game without requiring dedicated rounds and specific basis configuration, unlike CHSH-based DI-QSS schemes [Zhang et al., Phys. Rev. A, 2024]. Our scheme simultaneously certifies device-independence and key generation using a single test, achieving optimal performance for a seven-qubit GHZ state configuration. Security against collective attacks is analyzed, and a positive key rate is obtained under white noise and photon loss. Moreover, we show a bitwise advantage over the previous protocol for producing the same raw key length.