The Monroe Doctrine applies to European powers
China's main goals are economic expansion and shoring up popular support internationally - they're not as blatantly militaristic as the U.S. - and they're also not as deterred by some of the unspoken agreements between the U.S. and it's military allies.
The U.S. in fact does not get to dictate every aspect of South and Central America's policy, even though they would like to.
Also: I recall the Obama administration's repudiation of the Monroe Doctrine over a decade ago:
On Monday, John Kerry declared that “the era of the Monroe Doctrine is over.” Don’t believe him.
thediplomat.com
If this improves the lives of the average Peruvian person - to hell with the U.S.