"High Church" is really Anglican terminology, which has also been used in other Reformation traditions (e.g. "High Church" Lutherans and Methodists). I don't think it's necessarily about looking more "Roman." There are Romanizing Anglican High Churchmen, but then again there are also High Church Anglicans who look to the pre-Reformation English Church for guidance (e.g. Sarum Use), or to Eastern Orthodoxy (Phil-Orthodox).
Until the mid-20th century it didn't make much sense to apply to Roman Catholicism. These days, given the state of Catholic belief and practice in many places, it might be possible to refer to something like Roman Catholic "low churchmanship." Rather like the old Book of Common Prayer, the reformed Roman Rite can be celebrated in many different ways. It can be celebrated almost as a stripped-down, rather Protestant-looking communion service, or it could be celebrated in a way very closely approximating an old Tridentine High Mass.
It doesn't make much sense to apply it to Eastern Orthodoxy (I've never met a "Low Church" Orthodox).