Sort of but not entirely. Those audiophile terms are rather vague and can describe purely perceptual/physiological effects, while spatial audio is an actual physical audio difference. Spatial audio describes some form of surround sound, so the difference between (2 channel) stereo and 5.1 surround sound for example. Typically though, it describes a surround sound format that also includes height information, EG. A surround format with speakers above your listening position as well as around. Dolby Atmos being the most common example of such a format.
It’s not really a gimmick, it’s a real thing that has tangible benefits. How well it works and how well it’s been employed when it’s re-mixed/processed for headphone output is a different question though, which depends on a number of variables, including your personal attributes (such as head size/width and many others). And yes, it can be applied to game audio and other applications, such as VR for example.
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