StoneyB deals with of the first example very neatly. I would reiterate his point that, interpreted literally, "To appear to flash" says pretty much everything that "to appear to flash as if with light" says.
However, beyond merely offering that example, user37612 notes that it is a definition, presumably from a dictionary, and I have noticed that dictionaries often use "as with" as a space-saving compression of the phrase "as, for example, with." Indeed, Merriam-Webster's goes a step further, and uses "as" by itself as a short form for "as, for example," as in this definition of the verb leach: "to subject to the action of percolating liquid (as water) in order to separate the soluble components." I suspect that the relevant dictionary's desire to avoid spelling out "for example" explains the wording of the first example.
The second example, meanwhile, looks to me like an example of like-shyness: Perhaps as a result of unpleasant experiences with English teachers during their impressionable youth, many writers become afraid to use like in situations where even grammar purists would have no objection to it. Chief among those instances are sentences where the meaning in question is "similarly to." To evade the feared ignominy of misusing like, like-shy authors often resort to substituting "as with" for it.
If you replace "as with" with like in the second example, you can see more clearly a second problem in the wording (augmenting the problem of widely shared uniqueness that StoneyB pointed out): Nokia isn't merely like a large organization; it is a large organization. So the wording of the opening part of the sentence really ought to be "Like any other large organisation..." (I'm also not sold on the idea that organizations "collaborate" with their own employees, as opposed to treating or managing them in a certain way; but this is far afield from the question of how "as with" functions in the two examples.)