Cancer is not a single disease, but the term for a range of different diseases with the same ultimate symptom: cells that grow in an uncontrolled manner and which can invade other tissues.
Cancers can be caused by a huge array of environmental factors, but the tissue type where the cancer occurs will have different levels of environmental exposure. Damage by UV radiation, for example, is a common cause of skin cancer, but almost for cancers of internal tissues such as the ovaries, because the skin is the only tissue which is exposed to UV from sunlight.
In the case of stomach cancer, a variety of environmental cues suggest themselves, including diet and certain infections. However, it's impossible to pin down a single cause of stomach cancer, just like it's impossible to pin down a single cause for almost any cancer. The possible range of causes is too diverse.
So the literal answer is that yes, the cause of stomach cancer is unknown. But the question itself is not terribly meaningful.
EDIT: The OP asked if this meant there was no way of tracing a specific individual cancer back to its cause.
Not really - my apologies for a poor explanation of my point. The problem is more one of how things are grouped and classified. It's possible in occasional cases to discover the originial cause of a specific instance of cancer (the reasons why deserve an answer in themselves) - but because different individuals presenting stomach might have different root causes, you can't say that stomach cancer has a single cause.
Here's an analogy. Imagine there's an interruption to the internet service to your house. If it's short, you'll probably never know (or care) what the root cause is. But if not, there could be lots of reasons. Your router could be faulty. There could be a power out at the local exchange. An important pylon somewhere might have blown down in a storm. A shark might have chowed down on a vital ocean cable.
The question about stomach cancer is akin to asking "is the cause of internet outages known?" as though there's only one possible cause when there are many. And each individual instance can likely be traced to one of a number of different causes.
