The area on the map is technically not Alki Point. It is a beach area on the opposite side of Alki -- opposite of the traditional boardwalk area with the statue of liberty and so forth.
Are we still meeting where I drew on the map? That is where Scott is presumably expecting us to meet. The map location is nowhere near the boat ramp (about 2.5 - 3 miles away) and it is a little ways from the light house as well.