I worded that badly, since you clearly have explained the sense in which you are using the word. I am wondering, however, how your definition relates to the usual one. Is it a generalization? Or just plain different? For instance, would a SIC be equiangular relative to your definition (using SIC field norm instead of cyclotomic field norm)?
I am a little confused by this. As I use the term, lines are equiangular if and only if the "trace of pairwise product of (distinct) projectors is constant". You seem to be using the word in a different sense. It might be helpful if you were to explain exactly what is that sense.