The actual aircraft that crashed in that incident was a special modified version, the NF-104A. There were only two made, and they had a hydrogen peroxide rocket motor in the tail for the highest stage of the flight. They were designed purely for breaking the altitude record.
A couple takeaways: at :26 the pilots closes the canopy, but doesn't Costco it. On several "high speed" scenes, flaps & slats are deployed. Just sayin.
Germany had a hard time with the F 104 G. Post WW II, Luftwaffe stopped flying. Starting again with the F 104 G and few seasoned pilots, early aircraft and pilot losses were high. Germans nicknamed it "widowmaker" and it was for them. German demands on aircraft and pilots were very high with F 104 G performing roles outside it's design envelope and flying in darkness and bad weather. Other nations had losses but none so severe as Germany.