Is There Such a Thing as Immature Oil?

Yes, there are differing grades of petroleum deposits. Kerogen is organic matter that serves as the root material for conventional petroleum deposits. As this material is "cooked" by the internal temperature of the earth, oil and gas are generated. Material that has the potential to create oil but hasn't is known as an immature source.

Having not seen this particular film, King Kong may have been referring to a deposit that had not been suitably "cooked" to produce effectively through a conventional oil well. Realistically, unless there was an increase in temperature, there doesn't seem to be a reason why 10,000 additional years would be sufficient to produce oil from an already immature source.

They may have been thinking of something similar to portions of the oil sands of Alberta, Canada. The material will not flow unless additional heat is added to the system to evolve the oil and gas from the formation. In Alberta, some of the sands are shallow enough to be mined and treated at the surface, and some is produced using a much less invasive technology known as Steam Assisted Gravity Drainage (SAGD).

I recommend Norman Hyne's book "Petroleum Geology, Exploration, Drilling, and Production" for a non-technical introduction to oil and gas questions.

The oil and gas chemistry however remains the same in the oilsands, heat is added simply to separate the bitumen from the sand. Therefore I wouldn't consider it immature oil because it is a mechanical mixture of oil and sand. On the other hand it does require further refining and separation including a hydrocracking process in order to produce a premium product but so do many other sources of oil and gas.

jkster is right oil cannot be immature, it is either oil or its not and 10,000 years is not enough time to turn Kerogen to oil.

jkster107 you have a really interesting comment

Yes, oil shale could be called immature oil. Given enough time, heat, and pressure, it will eventually become oil. Given the time scale on which this happens though, it is unlikely that it would occur within 10,000 years unless it was already very close to becoming "usable".

'ain't dun yet, throw em back for a couple centuries,,

In case there is some oil underneath a younger layer of oil shale, but it is difficult to extract because of being asphaltic or having too great a sand mix, injection of carbon dioxide gas can help. Copious supplies of CO2 can be obtained from coal burning power plants that want to sequester the dreaded greenhouse gas under an impenetrable layer of oil shale.

While hiking in Algonquin Park, the guide made some interesting suggestions about the connection between beaver dams and oil.
The water in a beaver pond quickly becomes stagnant with almost no oxygen in it. Anything that dies and falls in to this water will not be eaten or decompose in the usual way, and will be preserved for thousands of years. Eventually, the pond or flood plain will become a peat bog, which is an excellent carbon sink, since it does not decompose the way a forest does. Now, throw an ice-age or 10 on top of that, and you eventually get oil.
Thank the beavers for oil.
I know it's not that simple, and that there are many origins of oil, but I'm a Canadian, and I like this one for now.

If a cake needs to be baked for an hour, but you take it out of the oven 15 minutes to early, it's not a cake, but you only need to bake it for another 15 minutes, not another hour. Sure it isn't oil yet, but it's in the process