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I understand a culling but this, as far as I know the definition, is not a culling (thinning of the herd for its own survival or for medical needs.)

This is the  killing of wolves as a predator of a favorite hunting species.  As far as I know, the Alaskan moose is not an endangered species or even close to being endangered. If they were moose hunting should be outlawed first.  

This makes me cry - it is just sad... very very sad for two majestic and beautiful species.

Removing animals from the herd to assist in herd improvement and maintain herd size. Selection criteria are normally based on factors such as disease, infertility, milk yield, etc.
www.specialistcheesemakers.co.uk/best_practice/Glossary_of_terms.htm

This is being done to benefit the herds health overall.  A difficult thing to do for sure, but necessary.