Personally, I feel like this is an accurate and descriptive term. Phase to phase voltage is typically 208 (220 nominally), , so when you only have one phase available it is 220 (240 actually)-but it is "split" into 2 110/120 volt legs. I understand that the term is often used with motors and that the mechanism involved there is different-but I don't think it leads to confusion.
I wish that article at least included the acknowledgement that 3 phase and split phase are different enough that there can be different considerations depending on the supply. Obviously, going into depth on the difference would be well beyond the scope of the article.