I suspect that these folk would be very surprised to learn that it is not, as they have been practicing it as one for a long time now:

http://global.sotozen-net.or.jp/eng/library/glossary/individ...

Although there is good reason to speak of the "Zen school" as a distinct branch of the Buddhist tradition of Japan, there has never been any organized social or institutional entity bearing that name. At present, there are twenty-two comprehensive religious corporations (hōkatsu shūkyō hōjin 包括宗教法人) registered with the Japanese government that are recognized as belonging to the Zen tradition (Zenkei 禪系). These include: the Soto School (Sōtōshū 曹洞宗); fifteen separate corporations that identify themselves as branches (ha 派) of the Rinzai lineage (Rinzaishū 臨濟宗); the Ōbaku School (Ōbakushū 黃檗宗); and five small corporations that have splintered off from the Soto and Rinzai organizations. Each of the twenty-two Zen denominations has a number of temples affiliated with it, ranging from 14,664 in the Soto School to 3,389 in the Myōshinji branch of the Rinzai lineage (Rinzaishū Myōshinjiha 臨濟宗妙心寺派), 455 in the Ōbaku School, a few hundred in the smaller Rinzai denominations, and just a handful in the smallest of the corporations (all data from Bunkachō 文化廳, ed., Shūkyō nenkan 宗教年鑑, 2003 Edition).

One thing that clergy affiliated with all the Zen denominations in Japan hold in common is the belief in a Zen lineage (Zenshū 禪宗) of dharma transmission said to have been founded by the Buddha Shakamuni, established in China by the Indian monk Bodaidaruma, and subsequently transmitted to Japan by numerous Japanese and Chinese monks. During the Kamakura period (1185-1333) and the two decades immediately following, by one account, some twenty-four separate branches (ryūha 流派) of the Zen lineage were established in Japan. By another reckoning, there were forty–six individual transmissions of the Zen dharma to Japan, beginning with Myōan Eisai 明庵榮西 (1141-1215) in 1191 and extending down to the Chinese monks Ingen (C. Yinyuan 隱元,1592–1673) and Shinetsu (C. Xinyue 心越, 1639–1696), who came to Japan in 1654 and 1677, respectively, and established the so-called Ōbaku lineage (Ōbakushū 黃檗宗). At present, however, all Zen clergy trace their own lineages of dharma inheritance back to China through only two men: (1) Nanpo Jōmyō 南浦紹明 (1235-1308), a.k.a. Daiō Kokushi, founder of the Daiō branch (Daiōha 大應派) of Rinzai Zen; and (2) Dōgen Kigen 道元希玄 (1200-1253), founder of the Dōgen branch (Dōgenha 道元派) of Soto Zen. All the other branches of the Zen lineage that flourished in the past are said to have died out, having failed at some point to produce any more dharma heirs.

Most of the Zen denominations in Japan operate training monasteries in which the bureaucratic structures, ritual calendars, and modes of practice are modeled after those found in the leading Buddhist monasteries of Song (960-1279) and Yuan (1280-1368) dynasty China. Those institutional forms were first imported into Japan in the Kamakura period, chiefly (but not exclusively) by the same monks who transmitted the Zen lineage. Texts containing the religious lore of the Zen lineage in China - genealogies of dharma transmission, biographies of Zen masters, records of their discourses, and koan collections - were also brought to Japan at that time, and have been handed down to the present within the various denominations as the common heritage of the Zen school.