Is the bullet train in China typically cheaper than taking a domestic flight?

This depends a lot on the specific route: let's look at a typical example: Shanghai to Shenzhen. In early February that's about $93 for most trains and you can get one way flights at around $94, so it's basically a wash.

At this point it really comes down to travel time (10+ hours on the train, 2.5 hours on the plane), convenience of departure & arrival locations (train station vs airport) and schedule. Maybe the train is better if you take a sleeper car and save one night in a hotel.

On the other hand if you look at Shanghai to Wuhan the train will be lot cheaper since it's shorter and not a particularly popular flight route.

Keep in mind that flight prices have almost nothing to do with distance anymore. Wuhan is only half as far from Shanghai but the flight is almost 3 times as expensive. It just turns out that SHA->SZX is more popular and has more competition which keeps the price low.

Any "general" statement about flight prices is bound to be wrong and you should always check your specific route and dates.

https://www.chinahighlights.com/travelguide/transportation/plane-or-train.htm claims that the price comparison bullet train vs. flight depends on the length of the journey:

Also, from the 2020 study {1}:

With the development of more high-speed railways, HSTs [high-speed trains] have played an increasingly important role in the inter-city transport market because of their advantages in saving time compared with conventional trains and lower price compared with air tickets, as well as their punctuality, comfort, and energy cost. HSTs are have been regarded as a competitor to air travel especially in short- to medium-haul transport (Campos and De Rus, 2009, Clewlow et al., 2014, Martín et al., 2014, Yang et al., 2018a, Yang et al., 2018b).

References:

• {1} Wang, Jiaoe, Jie Huang, and Yue Jing. "Competition between high-speed trains and air travel in China: From a spatial to spatiotemporal perspective." Transportation Research Part A: Policy and Practice 133 (2020): 62-78. https://doi.org/10.1016/j.tranpol.2019.06.010

In my experience, which is Beijing to Shanghai, the train has always been a little bit cheaper.

I mean, yes, the sources you cited are generally right. I'm speaking from experience here, so I don't have data, but I believe my experience to be generally reliable. For long distances, there are a lot (I mean a LOT) of discounts on flights, but hardly any for the railways.

I picked a random date and a random pair of large cities that are quite far away from each other, say Changsha and Beijing, June 18th. The cheapest flight is 500 CNY and cheapest bullet train is 649 CNY, so indeed the flight is cheaper.

In fact, I originally chose Guangzhou to Beijing, but due to the current epidemic situation in Guangzhou, the flight prices were negatively influenced (the flights are as cheap as 300ish yuan, due to very low demand perhaps).

But for mid-ranged trips, e.g. Shanghai to Beijing, the cheapest bullet train is 498 yuan and the cheapest flight is 568 yuan, so it does not really make a huge difference here. However, the cheap flights fly into Daxing, which is really far from the city center.

Time wise, even if one add the time required to travel to/from the airport, and the extra time required to board a plane, the airplane is still almost always faster. HSR stations are often also far from the city center, and there's also a line for security, so there isn't much of a difference here.

But often, for medium distances, the best deal is (at least used to be) the sleeper train. Sleeper trains are quite fast (the Z and T trains can run up to 160km/h), and since they run at night, you don't "waste time". I used to be a frequent passenger on the T32 sleeper train, travelling from Nanjing to Beijing W. It's dirt cheap and there's a kitchen on board for late-night cravings.

Unfortunately, like many other Z/T trains, T32 has been replaced D32, operated using CRH trains. The D sleepers are more comfortable but more expensive, making them less competitive than their Z/T counterparts (but you still save lodging!).