The conclusion in the "instructable" that you don't need an RTC for accurate timekeeping is not very well supported imho.
Many Arduinos use a ceramic resonator instead of a crystal. These have a tolerance of around 0,5% (1 second in about 3 minutes).
Even crystals age, that it their frequency changes slightly with age. The better RTC chips (say DS3231) include an age compensation.
Apart from all that, one of the main benefits of an RTC is the battery backup so you don't have to reset the time after a power off.
Finally, RTC modules can be had for half a dollar. So the matter is hardly worth discussing.
I have had several similar modules with the model numbers ZS-042 abd DS3231. These were advertised as having a rechargeable battery but actually came with a non-rechargeable battery which can, when the circuit is powered at 5 volts, explode.
Ignoring that minor detail, the clock modules keep excellent time.
In mine, I remove the resistor in the charging circuit and use normal CR2032 cells for the backup (see picture).
I have made an Arduino clock to work without an external RTC, but I included two buttons so you could set the time by hand. Later, I added support for an external RTC, but my clock will still run without one.
I have built a couple of clocks using esp, Wemos mini to be precise. Used Time library with code to get time from ntp server once per day. These appear to keep time very accurately. One is a chiming clock. It chimes within a second or two of the time signature (the "pips") on the radio. On the other hand, the radio is DAB, and they lag behind the live broadcast by a few seconds.