Lots of good answers so far! I'll concur on the notion that your point system is in fact a currency system, but I disagree that it is a fiat system.
The US dollar, the UK pound, the euro as presently understood as either a piece of rag paper, a little copper and brass disc or an electronic blip in an account, is indeed fiat currency. It is worth one dollar or pound or euro because the government concurs with the Central Bank who says those things are worth money.
Your system is actually quite different. You country's currency points (CPTS) are much more like Ithaca Hours which is a money system based upon a person's labour. If you work an hour, you get an Hour. In your system, if you work an hour you get 0.625 CPTS for four 40 hour weeks. (100 per month, as a generic construction worker.)
Where your system I think can be made to work is with the two factors that don't seem to have been addressed. One is the oil rich nature of your economy. Second is the very small size of your population. A million citizens sitting on top of decades or centuries worth of oil reserves means there's a lot of money to be made.
Just not by your citizens.
For this to work, two things need to happen. One, you need to control how many people can play in the sandbox at once. You can't have foreigners coming in and claiming, even after a couple generations, to be citizens. To keep your benefitted citizen rolls manageable, you need to define a citizen in terms of clan or family residency within the kingdom before the time of oil discovery. This means all the FDWs (and their inevitably domestically created children) are excluded; foreign oil execs & foreign service providers are excluded. Keeping the numbers manageable means your government should be able to provide all the basics free of charge in perpetuity.
Second, your Government Oil Corporation needs to be able to operate internally and externally with some kind of internationally accepted currency. US dollar, sterling, euros, gold sovereigns, ameros, Maria Theresa thalers, whatever. This is what they will get in exchange for the oil. This is what they will pay the foreign workers with. This is what they will use to import goods and build up infrastructure.
So long as conditions are reasonably stable and oil remains a valuable commodity, your system should function, simply because GOCorp has enough income to make the system work.
For a while. And for some people only.
The limiting factor will be in your citizens. Any citizen who is willing to abide by the limitations of the system ought to be happy. He gets a nice apartment all furnished and with a decent modern appliance plan, utilities paid, public transport paid, a good job, school for the kids, low cost public amusements and educational facilities at his disposal.
But what if his neighbour wants to visit Paris or tour London? What about the CPTS engineer who gets 200 a month who's friends with a foreign services engineer whose wage packet is full of exotic and valuable euros and silver thalers and US dollars? While the citizen has to use up his CPTS locally within the month, his friend can literally sit on a hoard of valuable money that doesn't expire!
Sooner or later, dissension will arise. GOCorp will have to manage the crisis somehow, which I leave to you!
YES your system can work; but only with limitations on who can benefit from the system and only so long as the citizens perceive the system to be of benefit to them. You'll need more social engineering than economic policy to keep the system working.
A possible outlet for your citizens who are not earning money, is to install a vending machine like this one:
This way, citizens can actually accrue some savings. Just press a button to determine how many CPTS you want to convert and the machine spits out gold or silver coins of equivalent value (less conversion fee).