Is gym exercise is beneficial for health?

YES!!!: Exercise, whether in or outside the gym, is one of the most important strategies for maintaining and improving both physical and mental health. For details see http://www.Hsph.Harvard.Edu/nutritionsource/staying-active-full-story/ ; http://www.Huffingtonpost.Com/2013/03/27/mental-health-benefits-exercise_n_2956099.Html ; http://www.Cdc.Gov/physicalactivity/everyone/guidelines/adults.Html.

Very much so: Any exercise is beneficial whether it takes place in a gym or at home, inside a building or outside in the fresh air.