The most clear way to write this sentence would be "The rest of the class has to guess which action that student is interpreting." or "The rest of the class has to guess the action that this student is interpreting."
Because you used "which" right before the object "action", you do not need to include the article "the". Some other examples of this:
"Which man" (correct) vs "Which the man" (incorrect).
"Whch place" (correct) vs "Which the place" (incorrect).
You also cannot say the "is" before action because it is already located at the end ("... is interpreting"). A way to detect this problem is to rewrite the section of the sentence
If you rewrote "which is the answer that this student is interpreting", you would get "This student is is interpreting which the answer". (incorrect)
If you rewrote "Which answer that this student is interpreting", you would get "This student is interpreting which answer". (correct)
I hope this helped :)