Hi there,
You cannot purchase a ticket from Kawaguchiko to Takayama in Shinjuku Expressway Bus Terminal.
However, if you are going to Kawaguchiko, you can purchase the ticket to Takayama at the ticket office in Kawaguchiko without reservation on that day.
You should be able to purchase the ticket from the following link below though...
https://www.highwaybus.com/gp/inbound/inbRsvBusStopSearch?q=kawaguchiko&p=1#routeSearch
But, the the ticket from Kawaguchko and Takayama is always available, so you do not need to make a reservation.
I hope you enjoy your trip in Japan!
Japan Trip Search