They did went to East historically : a good chunk of Central Asia was inhabited bye PIE or PIEzed populations such as Tocharians but as well some southern Siberian presence as far as modern Mongolia, such as with
Tagar Culture which is potentially tied with Iron Age Scythians. It's been theorized that some (really limited and hypothetically) features appearing in China may have some roots into a IE presence amisdt Proto-Turko-Mongol and Altaic peoples.
So, this is pretty much IOTL, but I think the real question would be why didn't PIE blossomed in Asia and why didn't IE peoples expanded from the Chalcolitic situation into Bronze Age Asia as it happen in Europe.
Why?
First, we're not really speaking of an invasion, such as a planned and necessarily militarized expansion in all Europe. The initial suspected migrations took place during Neolithic/Chalcolitic period for reaons yet to clearly determinated but probably tied to climatic change (which generally put a stress alike on farmers and pastors but with the latter being more able to migrate with their cattle), they went pretty straighforward about this (in a period where Proto-Anatolian peoples doesn't seem to have yet mastered horse domestication IIRC) and went in a slow road southwards. With deterioration of climate, migrating groups still continued to go relatively slowly forward in Europe outside the Pontic Steppe getting more differenciated with time and less "typically" IE as they adapted to their new conditions
You did have PIE peoples going eastwards, but the main idea is that the Pontic Steppe was less homely than it used to be, and as such the general trend was that it made more sense for most of people to go South or West.
Still, pre-Tocharian peoples, and eventually another branch of IE peoples with Iranic Sycthians, were largely present in South Siberia and Central Asia at some point, so it's not enough of an explanation to point to the slow movement that favoured a western/southern direction (IRRC, it's not even really a given that in PIE notions, both cardinal directions weren't associated).
Well, you had other peoples, that were relatively close to PIE own way of life : namely Proto-Turko-Mongols. When they met, it seems that at least part of both groups intermixed relatively easily possibly becaue of their similarities, which might have (ironically) cushioned IE presence (which if dominant, couldn't count on being "reinforced" by other IE peoples migrations giving the distance).
And when migration time kicked in (generally for similar reasons, altough social unstability in now constituedstates did played a role at this point), well rivality might have been an issue, and maybe as importantly, the neighborhood wasn't what it used to be. China was there to stay.
A bit like Egypt in Africa, China wa sable to boradly withstand raiding and campaigng bands (such as "Sea Peoples") or failing to do this, integrate them (Hyksos or Libyans). So it was either acculturation, either being stuck where they were, or simply going elsewhere (Yuezhi in Central Asia, Scythians in Europe).
The migrations out of Siberia might have played a role into the last development (especially giving we're talking of fairly small populations), the Mongolicisation and Turkification of Siberia in a first time, then the same in Central Asia.
So, there's a lot of reasons why PIE peoples didn't really had a go at Far East. But it doesn't mean it had to happen exactly like this. Obviously, the climatic causes of PIE and IE migrations in Central Asia and Siberia are hard to get rid of, so the most "workable" change we have is China, and namely preventing the rise of a Chinese imperial state : it's not going to be easy but for the sake of the discussion, let's assume it's done. What do we got.
Well...fairly small IE peoples (at this point, we can't talk of PIE, really) in rivality with Proto-Mongols and a sphisticated enough Sino-Tibetan ground population. And contrary to what happened in India, the prosperous part of the land wasn't right next to the entry of the region, which was fairly small.
We might see in a wild TL a Tocharisation and/or Aryanisation of Southern Siberia (as Proto-Mongols and Proto-Tungisic peoples might have been more interested in Korea and a good part of China ITTL), a surviving Tocharian (possibly Aryanised IMO) Tarim Basin, and a possible IE presence in Qingai, Sichuan and chinese plateaux overall. How much is anyone's guess, but I wouldn't expect India 2 there, probably something more mixed linguistically.
Now this is a complex topic, and might have mixed things there, so anyone can feel free correcting me on this.