Cannot understand the structure of a sentence.
The kind of journalism that insists on clinging to time-honored forms of reportage is languishing insofar as it fails to exploit social media. At the same time, were a traditional news service, by whole-heartedly embracing the Internet, to disregard the very tools that allowed for its ascendancy in the first place, it would likely suffer a similar fate.
What kind of clause is the sentence ' were a traditional news service' ?

Question

Cannot understand the structure of a sentence.
The kind of journalism that insists on clinging to time-honored forms of reportage is languishing insofar as it fails to exploit social media. At the same time, were a traditional news service, by whole-heartedly embracing the Internet, to disregard the very tools that allowed for its ascendancy in the first place, it would likely suffer a similar fate. 
What kind of clause is the sentence ' were a traditional news service' ?

Answer

"Were a traditional news service [...] to disregard" basically means "if a traditional news service disregarded [...]" but stressing the fact that it is (or ought to be) pretty unlikely, or purely hypothetical. Or they just want their sentence to sound more important than it really is.

I suppose the term may be subjunctive mood conditional. Hopefully somebody can give you a more targeted answer there.

But this particular pattern with the inverted verb is rather formal sounding. For example:
1) "If I were you, I wouldn't disregard it." 
2) "Were I you, I wouldn't disregard it."

Notice how the second phrase doesn't even have "if" in it. You can find similar inversions with "should", "would", and "had" as well.

Answer

I don't know the precise designation for the type of clause, but this is the subjunctive being used as conditional. Similar examples:  "Were he to ask for my help, I would gladly give it."  "Were it to rain all day, we would have to move the party indoors."  "If I were you, I would start studying now."

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