Can I buy High speed raill tickets at Beijing Airport for jouneys to other Cities in China

Sorry, you can't. You can book online through China Railway official app 12306 or through TravelChinaGuide hassle-free on this page: https://www.travelchinaguide.com/china-trains/
You can also go to the train station to buy at the ticket office but it's not guaranteed you can get one because they may be sold out by the time you are there.