Private pilot reported after landing; while taxing down the runway to exit; they observed another aircraft opposite direction taking off without making calls on the CTAF. The departing aircraft took evasive action to avoid a collision.

Narrative

I was PIC of my aircraft coming into land at HYS. I announced over the CTAF 10 and 5 miles from HYS of my intentions. Announced crossing over midfield entering a left downwind for 34. I heard Aircraft Z announce they were taxing to RWY 34 via Mike. So I know I was on the correct frequency. I announced turning left base as well as final for 34. My passenger nor myself NEVER heard any other radio traffic besides Aircraft Z taxing. Landed on 34 and did not exit at the first available off due to staying clear of Aircraft Z so wanted to taxi down the RWY to exit behind them. Before I had reached the exit I noticed a Aircraft Y approaching head on coming down the RWY. The pilot of Aircraft Y made NO traffic announcements. He had pulled up approximately 100yds in front of my plane and had banked hard left only 20' AGL. A bystander said they heard all of my traffic calls starting at 10 miles out. They said the pilot of Aircraft Y probably never heard any of the calls as they had started the plane and instantly began taxing to the RWY.