This usage is not a universal in modern English.
American dialects typically refer to a doctor's office as the building and/or room used for examination. The building may also be a clinic. The room itself may be called an examination room or, in most informal spoken English, an exam room. If the doctor is practicing within a hospital, they have an office in the hospital.
Surgery is a specialized term in the USA that typically describes only the branch of medicine related to cutting people open for repairs or examination.
From the American Heritage Dictionary on surgery:
- The branch of medicine that deals with the diagnosis and treatment of injury, deformity, and disease by the use of instruments. 2. a. Treatment based on such medicine, typically involving the removal or replacement of diseased tissue by cutting: The athlete had surgery on his knee. b. A procedure that is part of this treatment; an operation: The doctor performed three surgeries this morning. 3. An operating room or a laboratory of a surgeon or of a hospital's surgical staff: How long has the patient been in surgery? 4. Chiefly British a. A physician's, dentist's, or veterinarian's office. b. The period during which a physician, dentist, or veterinarian consults with or treats patients in the office.