Despite your best attempt to join in time by tendering resignation, the process has been delayed and you have been relieved on 8 th of Aug where as the joining date was scheduled on 5 th of August. In the meanwhile, you got an extension of two months in connection of your joining it means you can join by 7 th of October.
In the event of joining within the stipulated period as indicated above, there is no harm since you have been allowed to do so.
However, I am looking the same at a different angle. You were in a government department previously and moving to a government department and if you can maintain continuity of service period, so that there is no breakage of service between the two, you will enjoy all sorts of facilities without having interruption in between. In that way, your seniority won't be affected despite joining a new department and even your promotion in the new department will take place considering your date of joining of the first department. Your PF accumulation is not going to be discontinued under that event.
You will be deprived of all the privileges, if you fail to maintain the continuity of the period.
Since you have been given two month extension, you can join your job during the permissible period except the deprivation of the privileges as stated above.