I notice that the Air Force rules for an F-117 landing without using the
drag chute require a runway of at least 10,000 feet and an arresting
device at the end of this 10,000 foot runway.

The minimum runway for takeoffs by rule is 8,000 foot.

Even a 737 can do better than this. Why is the runway requirement
so long?

See http://www.fas.org/man/dod-101/sys/ac/docs/17v3.pdf
rule 2.2.3 and 3.20.