As your link states, "Despatch" (with an "e") is used "about a third of the time" in current English. (Age is also irrelevant as words get passed down for many years even after newer words begin to take over). As you will see from the following 2015 UK and US wepages, this variation is used in walks of life in today's world:
"Our client is a global provider of aircraft component services working out of a brand new purpose built facility in West Sussex. They now require two permanent employees in the Goods DESPATCH team."
http://www.aviationjobsearch.com/job/goods-despatch/3293189"At Document DESPATCH we are dedicated to ensuring that our customers receive the best possible level of service. We have the infrastructure, processes and commitment to exceed expectations."
http://www.documentdespatch.com/"Second DESPATCH"
http://democracy.islington.gov.uk/documents/b8244/Second Des..." Time will be allocated for the applicant to follow the jobs whilst on press and into the finishing department and then into DESPATCH ready to be received by the customer."
https://www.linkedin.com/jobs2/view/66284252?trk=jserp_job_d...