I had a look at that website and it says :
Unique material – experienced process
The strips obtained by molding have a profile with a more regular geometry. That is why we use this method instead of extrusion for the manufacture of the KLEMATCH

cushions.
The cushions’ profile regularity
obtained by molding allows players a game with greater accuracy. A molded strip manufactured from the finest rubber mixtures like a KLEMATCH

cushion, allows players to combine performance and accuracy for optimum satisfaction with a maximum service life.
this page says a bit about types of rubber and the molding process.
Research the types and uses of rubber molding. Learn about neoprene, foam rubber, grommet edging, silicone rubber, and the other types of rubber molding.
www.iqsdirectory.com
here is some comparison between natural rubber and synthetic rubber
Whether you’re a company leader who’s choosing materials for your products or a consumer who’s making buying choices for your household, learning about your options is the first step.
www.yulex.com
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I cant' speak for this particular manufacturer, what we do know is that natural rubber has some different properties.
I worked in a plant that recovered printing rollers , I used to remove the old rubber and prep the core and put it into molds. It was pumped from a drum and cooked in an oven in the mold
the OEM rollers were, I believe, mainly natural rubber, one of the properties is that it is slightly porous which gives it a grippy feel, like an elastic band or a pencil erasor. The synthetic rubber is less prone to attack from the chemicals, solvents and is cheaper to produce as it can be molded easily. It's cheaper and breaks down less quickly from ozone.
natural rubber is from rubber trees, most others are from the petroleum industry.
what I have seen is that the friction difference is substantial , so if a roller is driving paper you want that grippyness, If it's slick like an O ring, it wont drive paper so well. the slickness of the synthetic rubber was a bit of a disadvantage but it can be molded as heat cures it once in a mold.
One example where the grippynes matters, is a folding machine where paper is being driven by rubber rollers. If they are slick rollers made from basically rubber like plastic, they loose their capability of having drive as soon as they get dusty.
I noticed that when looking at rubber for pool tables, there is a lot of offshore stuff made of synthetic rubber, cheap stuff from china , It can be molded cheaply. I believe that making pool table cushions by extrusion, like in the brunswick video requires a much higher cost equipment setup than a simple heat activated molding process,
this video shows the Brunswick Superspeed manufacturing process, you can see how costly and unique the equipment required ot do that is.
If you are choosing a manufacturer for pool table rubber I'd take into consideration their process and what type of rubber they are using, some companies may be secretive about their proprietary processes.
I have occasionally looked into having real rubber rollers made, where synthetics would not work well , an example is driving wood through a thickness planer. It needs that grip that natural rubber provides. a slick synthetic roller will get covered in wood dust and slip.
It is expensive they have long wait times and I once went to the plant and was interested about their process but they wouldn't let me see inside, protecting their proprietary process.
I wont speak for or against a particular manufacturer, I just think they type or rubber you choose and weather of not it is natural rubber is important. when I see its made by a molding process and not an extrusion machine, it lead me to think this is using a synthetic but that may not be completely justifiable. a chemical scientist that studies rubber types and has in depth knowledge of different manufacturing types would definitely be able to shed more light on why certain types of rubber are best for pool table cushions.
If you are ordering rubber through online dealers, id just be a bit cautions that the rubber you are getting is the type of rubber most suitable. If it's incredibly cheap it's likely made by a molding process and not natural rubber.
i suspect that the machinery that Brunswick is using , although very dated looking, may still be in use and without knowing more I'd be a bit more tempted to go with that type of rubber or a manufacturer using similar extrusion equipment. Natural rubber, not plastics.
Its a big subject, I dont know everything, I'd like to learn more. I believe the type of rubber and the process used may have a large effect on its bounce characteristics.
One thing Im curious about, how much is the type of rubber affecting the drive between ball and cushion, when you spin balls into a cushion? The cloth separates the two, does the grippyness matter ?