Zustand is "condition" in the sense of "state" -- e.g. the condition of a patient is how well they are doing health-wise (in a stable condition, in a critical condition, etc.).
Bedingung is a condition in the sense of "if" -- for example, "You can have dessert if you finish your vegetables = You can have dessert under the condition that you finish your vegetables" (Du kannst Nachtisch haben, wenn du dein Gemüse aufisst = Du kannst Nachtisch haben unter der Bedingung, dass du dein Gemüse aufisst).
Can 'zustand' refer to health condition too?
zustand (lowercase) means something quite different -- it's a verb form of zustehen and means roughly "deserved" or "entitled". (Er nahm mehr, als ihm zustand = He took more than he was entitled to.)
This sentence contains the word Zustand (a noun), and this can indeed often refer to someone's health condition -- which is how I would understand it in this sentence.
Similarly, one might hear Sein Zustand ist stabil "His condition is stable" about an accident victim, for example.