Changing jobs to another company with similar activities

Look; as a general rule of thumb, when you resign from a company, the only papers you need to sign are your resignation and acknowledgement that you have received your dues

Restrictive competitive covenants such as the one you mentioned above are complicated.  In most of the GCC they cannot be enforced.  For these to be enforced, it has to be usually a defined period and a defined geographical area.  And for the company to claim compensation, it must prove that it suffered damages due to your actions which is next to impossible to prove.  However, since you are in the same country, the proceedings may still disrupt your new job.

Secondly, even if these are part of your initial contract, you should not have to sign a paper when you are leaving. The only time that happens is when the employer is giving you a separation package i.e. extra money on top of what you are owed and wants this in return.   As far as the final settlement is concerned, it is legally your right as per the labor law i.e. indemnity, un-availed leaves etc.  This has got nothing to do with signing or not signing that paper. 

Have they said that they won't pay you unless you sign?

If so, take a copy of that paper and go to Ministry of labor in Isa town  and get their opinion.  After that approach the employer with a refusal to sign quoting the MOL opinion on the matter.