This latest standoff is more about what is going on inside these countries and less on the relationship they have with one another.
Right now, regionalism is growing within China. Tibet has traditionally been one of the regions that has had and sought greater autonomy from the rest of China. With the growth of regionalism elsewhere, that sentiment has grown. Tibet also has a greater pull with India.
China’s military presence in the Doklam Region (which is pretty limited) is less to do with a potential conflict against India or even its non-diplomatic relationship with Bhutan than with trying to secure Tibet and keep it in the Chinese fold.
By showing off its military in the border region, China is also trying to boost patriotism and unite its own people against a potential adversary: India.
This is a tactic that has commonly been used by China to tackle its internal divergences, such as in the South China Sea.
The Chinese don’t want a war with India. There are already disputes in the South China Sea and escalating tension on the nearby Korean Peninsula. China (and any country for that matter) can't afford to have so many potential frontlines right at its doorstep.
India also doesn’t want a war with China. India is also experiencing increasing regionalism, with its own internal divergent problems. Sikkim, an Indian State near Doklam, is culturally very different than Delhi. Really, India is like a hodgepodge of informal states, each with very different dominant languages and cultures.
Sikkim is also a very young state in India, having only formally joined the union in 1975. Sikkim, along with other states like Assam and Meghalaya, are only connected with the rest of India by a very narrow passage between Nepal and Bangladesh. It’s an imperative for India to keep these states secure because no matter how remote a possibility, if the Chinese military did breach the border they could reach this passage and seal it off.
So this latest stint reveals more about what is going on domestically in these countries. There is an iron wall in between them, and with the internal stresses building up in both, they are even less likely to afford being drawn into a conflict that would hypothetically be catastrophic for both sides.