Tourist,
I can only take a guess here as my only aviation "real life" was in airline ops.
Looking at the google page it says
"The NF-104A was able to reach great altitudes through a combination of zoom climbing (trading speed for altitude) and use of the rocket engine. A typical mission involved a level acceleration at 35,000 ft (11,000 m) to Mach 1.9 where the rocket engine would be ignited, and on reaching Mach 2.1 the aircraft would be pitched up to a climb angle of 50-70° by carefully applying a load equal to 3.5 g."
So could that installation angle help to gain the AoA required for the zoom climb and speed, rather like a rocker elevator?