Exactly. It has four lines/poles, with two phases: one between each pair.
With four lines and the neutral you have four unique pairings/voltages of the same magnitude. Four line-line voltages in one system, and four line-neutral voltages in another system of equal magnitude voltages.
With three lines you have three unique pairings/voltages of the same magnitude. Three line-line in one grouping and three line-neutral in another grouping.
Consider again the 5-wire two-phase system. There are actually four phases present and is noted in engineering references to be more accurately described as a four-phase system. Still gets the "two-phase" label.
Set that aside for a moment and consider the two-phase system where you only have two ungrounded lines of the 5-wire two-phase system: looks like an even "L" or corner. Two lines and one neutral. Here you only have one line-line voltage but it is still labeled a two-phase system. It also has two line-neutral phases.
Now look a the OP system where you also have two lines and one neutral but a different phase separation. It is labeled a network system but is also commonly called a single-phase system. Just like the two-phase system you have one line-line voltage and two line-neutral voltages. The only difference is a 120 degree difference vs. a 90 degree difference.
Think about it: the same number of voltages but a slight difference in phase separation. One is called two-phase and one is called single-phase.
So I'll repeat it once again: the label does not always accurately describe the physical system. It is just a label.