Hello Sai. No GATE exam is not the only way to get admission into M.tech courses in India. Various institutes conducts their respective tests for their colleges. Some of those tests are:

• TANCET 2019- Conducted by Anna University for admission to all Tamil Nadu colleges.
• PGCET Karnataka 2019
• PGECET TS & Andhra Pradesh- Conducted by Jawaharlal Nehru Technological University
• VITMEE- Conducted by VIT Vellore.
• SRM Graduate Engineering Test- Conducted by SRM University
• MU OET- Conducted by Manipal University

Hope this clarifies your doubt. For further information comment down below.

Good luck!

Absolutely no, the exam isn't compulsory. You can easily get admission into any good private college for M.Tech if you have a minimum of 60% agrregate in your under granduation degree. But for IITs and NITs you need to have a good gate score card moreover gate can be helpful in many ways including the financial aspect because if you cleared gate with a good score and get admission into any government college then the fee structure will be very low as compared to the fee structure of private colleges. So I think you should give it a try. 

Hope it helps.

Thank you.