How is this figure supposed to be interpreted in the datasheet for the LM4766 audio amplifier, and determining the needed power requirements?
Please note the horizontal scale of the figure "SUPPLY VOLTAGE +/- V". This means that a 25 volt supply consists of +25 volts and -25 volts.

Your application of Ohm's Law is a good start, but you need to learn a little more about AC measurements. For a sine wave (and audio is always represented as such) the peak voltage is sqrt(2) times the RMS (Root Mean Square) voltage, and it is the RMS voltage which counts when computing power. So the most (audio) power a +/- 25 volt supply can provide with an 8-ohm load is (25 / 1.414) x (25 / 1.414) / 8, or 39 watts. Peak current will be 25/8, or 3.12 amps, while RMS current will be 25 / 1.414 x 8, or 2.2 amps. Of course, no real-world amplifier can produce a high current all the way to the supply rails, so the real power will be somewhat less than this. The graph showing 37 watts at 25 volts with a decently-low distortion figure indicates that the folks who designed the amplifier really knew what they were doing.