score:5
You're reading it correctly: domestic economy tickets on United do not normally include any checked bags. The same is true on most other US airlines, including American and Delta. The notable exception is Southwest, where two checked bags are included with all tickets.
International economy tickets commonly include one checked bag, and domestic first class tickets usually include two.
Also note that "basic economy" tickets do not even include a carry-on bag.
or is there some US custom that 1 bag is always included?
There is definitely not any such custom.
Source: personal experience.