Gabadinho's complexity index depends on the overall possible states (the alphabet) of your sequence. This is by definition. Here is an example based on your own one:
myseq <- t(data.frame(s1 = c("A", "B", "A", "C", "B", "A")))
seq1a <- seqdef(myseq, alphabet = c("A","B","C"))
seqici(seq1a) # 0.9594894
seq1b <- seqdef(myseq, alphabet = c("A","B","C","D"))
seqici(seq1b) # 0.854151
If you don't specify the alphabet when creating sequence data, TraMineR will use the different states existing in your data for setting it. So, according to your input data the alphabet may differ, and then you may obtain different results for measures depending on the alphabet.
To avoid confusion it is a good rule to always define explicitly the alphabet in which your sequences are embedded.