It's not really a technical term, it's a general, context-dependent phrase or figure of speech (think dairy). It just means the maximum or full version of something (i.e. not the reduced fat or "skim" version).
In your first link it's just referring to the more powerful bench configuration with two 580s. In the second link, though, it's used in the same way as Carfax83 described, in reference to the GPU die not being a cut-down one. And lastly, the article about FFXV on the Switch, the author there is stating that the game will be "full-fat" because it won't be a mobile version, but the full game as it is on other consoles.
There's probably a higher usage of the term in regards to GPU dies than other areas of technology, though, probably because some dairy-farmer-turned-chip-designer borrowed the phraseology and it caught on.