Even with 240 volt incoming service it still is considered single phase.
This installation is derived from one distribution transformer using mid connection between the two (240 volt) lines to get the 120-volt that splits the potential between the transformer winding, a split phase basically.
In order to get "dual phase" which by the way is not a term used by ANSI, NEMA IEEE. Instead ordinary Joe would call it Dual Phase.
The usual tech term for dual phase is "two phase" which is derived from two totally separate power sources (i.e. two transformers, two generators etc.) ...no intermingling of the two power sources. This setup is common in industrial heavy demand load like 50-100 horsepower motors. Crushers for cement aggregate plants for example. Steel forging plants with those heavy hammers.
In my effort to not appear being pedantic, I have no problem reading between the lines. . . at least (I try hard) because it gives me a good night's sleep. LOL
Confusing for some, but that's the way it's always been.