No. Your company is not correct. Gratuity has to be paid for the total number of years you have worked for them.

Did you take this job in 2001 under the sponsorship of the company? When did you get your ID card after joining?
If you had got the ID card in 2001, then surely labour contract would be signed by you in 2001, so the benefits should be paid to you from 2001.
If you had been working for this company with some other sponsorship, and then changed your sponsorship to this company in 2005, then you will have to accept what they have agreed now.

So, you are leaving Qatar for good?

All the best