攸 (yōu) is a classical particle meaning 'that which / what'. 存亡攸关 literally = 'survival or perishing - that which is at stake'. Functions as an attributive: 存亡攸关的 X.
register
Formal / written. Common in news editorials, speeches, and political analysis. The colloquial near-equivalent is 生死攸关 (shēngsǐyōuguān).