If the purpose of a resistor is to limit current, then it must be in series to a LED. Otherwise any single LED could thermal runaway and toast.
Here is an analogy....
Suppose you had three kids and you wanted give each $10 for the movies, would you put $30 on a table and trust them to take only their share? lol, no!
Yes, supplying each LED with its own resistor is going serial. Combining parallel AND serial is very common. My table has segments of 8 LEDs and a resistor all in series, but fourteen of these segments are in parallel.
There are many cases where you can get away with no resistors at all. Truth be told, resistors really do not control current (they only limit it for a given voltage). For real current control, something like a mosfet with a feedback loop is a way to go (they really are very cheap). But of course, the most efficient is connecting directly to a power source.
Its my opinion that resistor tutorials are for beginners, and as such should steer towards the safest design and most fool-proof (series, not parallel). This particular tutorial has many inaccuracies! For example, in series, there is no guarantee that voltage will be divided equally, only that each device will have the same current.
Honestly, it is not worth its ascii.
I highly advise either following a in-series resistor calculator, or learn basic electronics.
