It's a two-round voting system. It is, by definition, not FPTP.
There only functional difference between it and say, the original French two-round system that Maurice Duverger (of Duverger's law) contrasted with FPTP is that someone who wins an outright majority in the first election (an open "primary" in California) is not immediately elected.
The fact the second round is FPTP doesn't change the overall voting system. With only two candidates for a single seat, most voting systems degenerate to FPTP, but none of the issues related to FPTP are present either (there are no clones, no strategic voting, etc.)
There only functional difference between it and say, the original French two-round system that Maurice Duverger (of Duverger's law) contrasted with FPTP is that someone who wins an outright majority in the first election (an open "primary" in California) is not immediately elected.
The fact the second round is FPTP doesn't change the overall voting system. With only two candidates for a single seat, most voting systems degenerate to FPTP, but none of the issues related to FPTP are present either (there are no clones, no strategic voting, etc.)