What system can be called "embedded Linux based"?
I would call it built in if its purpose has been ported from a general purpose computer to a device or device that has a specific task. Also, the setup for this particular task should probably remove / disable / mitigate some other general purpose functionality (like starting it headless, disable / uninstall X, or publicly available tools / services to further allow the device to do its job.)
Basically look at the device and see if it shows up as "Linux machine" or "device that completes a specific USING linux task".
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I disagree that it has to be headless to be considered inline. For example, mobile phones are considered embedded, but they have video, i / o and what not. Personally, I find there is no clear line for inline. But in general, when you are working with minimal resources (e.g. minimal RAM) and doing very specific functionality (i.e. not general purpose) then it is more built in.
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Short answer: Yes
From wikipedia :
An embedded system is a special purpose computer system designed to perform one or more special functions, often with computational constraints in real time. it is usually implemented as part of a complete device, including hardware and mechanical parts. In contrast, a general-purpose computer such as a personal computer can do many different tasks depending on the programming. Embedded systems management are many common devices in use today.
While I think your device is not embedded on another device, I see that it has few features and is not a general purpose computer.
Also, as Shashikiran says, SBCs are commonly referred to as embedded systems.
The PC-104 drove me crazy a few years ago ...
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