In standard play, yes. The FIDE Laws of Chess taking effect from 1 January 2023, Article 8.1.1, require each player to record both sides' moves, move by move, as clearly as possible, in algebraic notation (Appendix C) on the scoresheet prescribed for the competition, or on a FIDE-certified electronic scoresheet. The duty pauses when a player has less than five minutes left and does not have 30 seconds or more added with each move (Article 8.4). Rapid games do not require players to record moves (Appendix A.2). Blitz follows that rapid rule unless the event puts an arbiter on every board and records the game (Appendix B).