score:3
As is common, the English website is useless and one must visit the Japanese one, which says that traffic on the JR Central portion of the Takayama Main Line, which includes Takayama station, is currently suspended between Sakakami and Inotani (see the station list). Substitute buses are available. The JR West section (Inotani to Toyama) is operating normally.
Regarding the Wide View Hida, it is currently not running between Toyama and Hida-Furukawa, so if you want to go through Toyama, you would first need to take an ordinary train from Toyama to Inotani, then the substitute buses to Sakakami, then another ordinary train to Hida-Furukawa and the Hida to Takayama (or possibly just ordinary trains from Sakakami to Takayama). If you go through Nagoya, everything is operating normally.
Full operations are scheduled to be restored in late November.
Upvote:4
The link you provided, says "This page shows you temporary closed sections by natural disaster... Substitute transportation service is available on most of closed section." Also, both JR West traffic info and JR Central train info (who share responsibility for the line) suggest there are (unspecified) problems on this line. No info when service will be resumed.
If you are not travelling until 4 Oct, you could risk leaving your booking until later to see if the route reopens, or book an alternative route.