Directly connecting LEDs to IC outputs
The article you link explains the arrangement fairly well. The 4017 has outputs designed to work with LEDs, and limit the current by the inherent characteristics of the FETs used. Graph from a slightly newer datasheet for this ancient device.



This shows what the current will be with different system voltages (determines Vgs) and Vds drop - which will be what is left between the supply voltage and the LED drop. For 7V (9V battery - 2V for a red/orange/green LED) it indicates about 17mA (matches up with figure 5 in the linked article). The datasheet states a limit of 100mW per output transistor - all the voltage dropped ends up as heat, and this is where the 8V limit comes from  (7V * 17mA gives 119mW if you run at 9V). To get around that you do need to use external resistors.  Practically, the 9V battery droops significantly with this load, and you can get away with it - at least I did when breadboarding these things several decades ago.