The claim is, at best, very poorly stated. No external sources are necessary to prove this. Consider the following quotes from the article:
There are 1.2 billion Muslims in the world today. Of course not all of them are radicals. The majority of them are peaceful people. The radicals are estimated to be between 15-25% according to all intelligence services around the world.
The claimant is drawing a line between "peaceful" Muslims and "radical" Muslims, claiming that 15-25% are radicals, while the others are peaceful.
This is re-enforced two paragraphs later:
"So why should we worry about the radical 15-25%? Because it is the radicals that kill. Because it is the radicals that behead and massacre," Gabriel said.
So the claim is that 15-25% of 1.2 billion Muslims participate in beheadings and massacres. That's 180,000,000 - 300,000,000 Muslims who are supposedly involved in beheadings and massacres.
Unless we are going to assume a huge media cover-up of Muslim-initiated beheadings and massacres, there simply are not enough beheadings and massacres to involve that many perpetrators.
Although that doesn't mean there's not some element of truth to such a claim--it only means the claim is made in very sloppy terms.
This post summarizes an article in The Weekly Standard, which in turn summarizes a book by John Esposito and Dalia Mogahed, which analyzes this issue, and includes the result of its own study, which defines a radical Muslim as
those who say the 9/11 attack was “completely justified,”, and this group
comprises 6.5 percent of the sample.
I can find no evidence to support (or contradict) the claim that "world wide intelligence services" support her 15-25% claim, but I stand by my belief that this is a meaningless claim anyway, as "intelligence service" is far too vague or ambiguous to possibly be meaningful.
TLDR The specific claim is confused, but with a properly-conducted survey, with meaningful definitions, we can determine how many Radical Muslims there are, and one such study found that number to be 6.5%.