Why do anti-trust regulators in China need to approve NXP's takeover? Qualcomm is currently awaiting Chinese regulatory approval for its acquisition of rival NXP.

Both companies aren't based in China. I'd understand that vehicles like tariffs can be used by countries to exercise control over certain trade inbalances, but how could government block a takeover taking place outside of its sovereignity? Are anti-trust laws of international nature, in some case?

Is the rationale behind this case the same as US technology companies operating in the European Union, with regards to anti-monopoly policy? No long ago, I recall Google being fined by the European Commission on monopoly charges with regards to some of its services in the EU. The case of NXP's takeover seems of an entirely different nature.
Generally, antitrust regulators have authority over any company doing business inside the zone of its control, hence why the EU antitrust regulators hit Google in 2017, or the EU's recent examination of US company Apple's attempted acquisition of another US based technology firm, Shazam.

Of course, for these companies, there's always the option of simply pulling out of those markets (not selling any goods or services, or holding any capital inside their borders) which dodges their authority. But given the size of these markets (US, China and the EU particularly), that's simply not a feasible option.