First I must apologise as in my haste to find out just what your card was, I missed the nuance in your question that stated (quite clearly, now I look at it again):
I am trying to use the card for certain games, and although the graphics seem fine, cinematics within the game stutter badly.
It would appear that it is not the actual horsepower of the card you are having a problem with, but the video decoder that is built into it.
Chances are that any cinematics are encoded using h.264, this is quite likely as it would afford the highest quality visual with the lowest storage space cost. Given the relatively recent cards that the Wolfenstein series state as their minimum recommended card (see below) it is entirely possible that they expect to be able to fully offload all H.264 encoding to the graphics card, as every card after the G80 that yours is based on has a full decoding pipeline for h.264. Certainly every card since those they recommend (the GTX 460) would be able to decode the video entirely on the graphics card.
Your card though is a halfway house, it has some h.264 decoding abilities but not all of them. The G80 that powers your card was made before the chip that powers the 8600 in the image below. In terms of video decoding ability if it equivalent to the Geforce 7 series:
image borrowed from http://www.anandtech.com/show/2220
Your G80 chip is lacking several key parts to allow your system to fully offload the very intensive h.264 decoding task to the GPUs PureVideo decoder.
Which means that the game will either be offloading all of the video decoding to your CPU or, at the very least, a substantial quantity of decoding. How much decoding it offloads is dependant on whether the games use their own methods to display the video or whether they pass the video to Windows to play.
Either way this means that the CPU is doing the task of decoding something. If the game itself fell back to a built-in software decoder, it could be one that is poorly optimised for multicore processors. I would actually be surprised if your CPU cannot handle h.264 decoding using its own brute force.
I'm not entirely sure why they would be stuttering, as they should be failing over to full CPU decoding and you should have enough grunt to be able to do it, my only assumption would be that it is somehow trying and failing to properly use the video decoder on the GPU as it expects a more capable graphics card.
Depending on how the game displays the video (internal vs external codecs) there may not be an easy way fix it.
The Quadro FX 5600 is not a fast card for either CAD or gaming, not by today's standards. It is the workstation equivalent of a Geforce GT 8800. This is the card that has the same chip as yours and it was released in 2007. This should give you one idea of why your card is slow.
While the 8800 is (was) not particularly a slouch it has been surpassed many times by more modern cards in a similar price bracket.
Suppliers don't tend to mark down their workstation cards in the same way that consumer cards do, this creates a false impression of just how fast a workstation card will be when compared to a consumer card.
Modern high end games also expect more grunt from a card than they used to. Your card claims to be about 500 GFLOPS of performance, a current generation high-ish card is around 1500 to 3000 GFLOPS or more.
To add slightly more insult to injury I had a look at http://www.videocardbenchmark.net and found your card in the "High Mid Range" cards with a score of 695. A current generation mid range card that I would expect to be able to play games comfortably on easily scores 4000+. I would recommend that site to anyone who a relatively quick idea of how one card will perform next to another for gaming tasks.
Wolfenstein: The Old Blood recommends a minimum of a GTX 560 for it to be playable. Going back to the list on Video Card Benchmark the GTX 560 has a score of 3117 and has 1000+ GFLOPS of performance along with a lot of DirectX 11 features like hardware Tesselation which can dramatically improve model detail with low performance cost. This probably means that on your FX 5600 the game will be nearly unplayable on all but the lowest settings.
Wolfenstein: The New Order has slightly more modest minimum requirements, only recommending a GTX 460, but this is still several generations newer than your card and will have a lot of performance enhancing features that your current card is lacking.
I am sorry, but your card is below minimum recommended specifications for pretty much all current generation games.
I would be interested to know where you got the card and, if you paid a significant amount for it, what their returns policy would be.