Those stall speeds are derived for specific conditions. In the case of that POH those speeds assume level unaccelerated flight, 2550 lbs gross weight, standard atmosphere and no wind. They are given as a speed rather than raw AoA because most non-aerobatic small airplanes lack AoA indications in the cockpit, while all have airspeed indicators. A non-aerobatic airplane also spends most of its time in the part of the flight envelope where the assumptions needed to list a stall speed tend to be valid.
The stipulation of level flight means the relative wind is fixed, thus the AoA depends only on the pitch attitude above the horizon. For an given weight there is a relation of pitch attitude required to maintain level flight for a given airspeed. Given these specific stipulations, you can determine the airspeed that results in the critical AoA being exceeded.
If any of the criteria listed above are not true, then those published stall speeds are not meaningful to you. You can stall at any attitude and at any airspeed.
To see the true relation between airspeed and stalling you need to consult a Vg diagram.
The curved lines starting at 0 MPH and 0 load factor represent the stall speed for a given load factor. The stall speed listed in PoH you quote is specifically the point noted "Normal stall speed" on this chart (this chart isn't for the same airplane, so the numbers will differ).