The report cites this (far more technical) 2009 study, in which it is pointed out that if we want to have a 75% chance of keeping warming by 2100 below 2ºC, then we can burn less than half the current proven economically recoverable oil, gas and coal reserves. That is, we don't need to do any further exploration, cannot employ any non-conventional sources (such as shale gas or tar sands) and of those that are already considered recoverable, more than half need to be left in the ground. That is a very pithy summary of the challenge, and gives a basis for attempting to focus the minds of decision makers.
The argument that the next ten years are the critical decade for climate has been made pretty consistently since the late 1980s. This has not been inaccurate, though as a message, it can become confusing when it keeps getting repeated with new goalposts. It is not inaccurate because the question is "critical for what?". Back in the 1980s, we had perhaps a decade to address the climate issue at relatively low cost and with relatively minimal consequences. Each decade of business as usual makes the costs of mitigation higher, the benefits lower and the chance of reaching results beyond our ability to adapt more likely. The time for action was long ago, but today is better than tomorrow.