They were avoiding the Tibetian plateau not China. The plateau is about 4000 m above sea level, 2,500,000 sq kms and does not have many airports. This makes it very risky for civilian aircrafts and almost everyone avoids it. Additionally, if you are starting from New Delhi, you have to fly over the Himalayas which is even riskier.

> They avoided flying over China

Sometimes it's easier/cheaper to avoid a country's airspace through a slight diversion than pay the overfly costs. Some country's ATC's can be kinda hostile/annoying/unprofessional/expensive. (I've heard China likes surprise military airspace restrictions that make flight planning annoying).

Plenty of routes that don't take shortest path for geo-political & artificial cost reasons (but you don't hear climate change activists raising issues with that much).

The original path was pretty close to great circle path. Its just map projection that makes it confusing

Russia and China combined are most of Asia - you can't practically avoid flying over both.