The premise is simple. Rudolf already had an older brother who had died in infancy (Ferdinand b.1551, d.1552), so if Rudolf were to die young - or at least before his dad does - how would this affect the Habsburg control of the Holy Roman Empire? Rudolf left one hell of a power vacuum according to his brothers. And besides his cultural and artistic legacy in Prague, Rudi wasn't (to my knowledge) politically active. Add to that his refusal to marry and have heirs, and his poor relations with his brothers (Matthias and Albrecht) when they married his intendeds or with Felipe II due to his almost-but-not-quite non-Catholicism, and more than one problem among the Habsburgs had to deal with in the 17th century.
So, let's keep everything else more or less on track until 1576 - Maria's womb still going like an overworked bakery, all kids are as OTL, Rudolf just dies soon after birth or within his first year (Rudolf was born in July 1552, while Ernst followed in June of 1553, so Max and Maria must've really liked each other).
Could/would the Habsburg empire develop along a different trajectory?