I think it has to do something with 'jargon' and that's the reason, the journalist has not included the definite article before the word 'government' [However, I'm coming up with an example where 'the' is used in such sentence structure].
To prove this point, I'll bring in two references:
David Marsh, Guardian Style, Guardian Books 2007 defines:
"Leaving 'the' out often reads like jargon: say the conference agreed to do something, not 'conference agreed'; the government has to do, not 'government has to'; the Super League (rugby), not 'Super League.'"
Taking this reference, I referred COCA, and was a bit surprised.
"....levels of government..." returned 395 results. Examples:
"...had powerful supporters at the highest levels of government."
"They relentlessly target the military, defense contractors and the highest levels of government."
"The levels of government include: a) federal (both) b) provincial..."
And so on...
On the other hand,
"....levels of the government..." returned 21 results. Examples:
"And so this is still being discussed at the top levels of the government."
"Al Qaeda had been communicated directly to the highest levels of the government."
"...perhaps even at the very highest levels of the government, who were making money off of this..."
So to answer this question, I think it depends on the 'author's style'. If the author puts article, it might be to avoid the jargon (Guardian style) but if he does not use, it's not incorrect.