Yes and no. Athlete tables, or sometimes called firing point stands, are required under international rules such as ISSF and USAS. The range manager though is given a great deal of leeway with respect to the design and dimensions of the stands to provide the athletes.
National rulebooks, such as the National Three-Position Air Rifle Council or CMP rulebooks do not require them. However, their use is common and helpful. Most particularly in the standing position, the athlete monitor is physically in arms reach which makes interacting with them easier.