Yes, it's the aroma.
Typically it depends on how sensitive each person is to each aroma compound, with each individual having different sensitivities to each compound.
The typical scale for strength or concentration of aroma for a given flavor as perceived by each individual's differing senses is as follows.
None detected (flavorless)< Mild note (washed out)< Normal strength as compared to typical western fruits (Your general description of spice)< Strong (Intense)< Very Strong (Resinous)< Overpowering (Medicinal)
What one person perceives as lying in one area of the spectrum, others may perceive the same sample in a different area.
The characteristics of the aroma (flavor) can also affect how the spice is described, with mangoes that have flavors similar to Alphonse often being described as having "spice" in the flavor.
Typically Haden is not described as having spice or a spicy aroma. It's often described as a "classic" flavored mango, as most in the mango growing region of Florida are quite familiar with its peachy aroma. Therefore it serves as a baseline for comparison to other mango varieties. If the common mango grown in the area is of a different flavor, the baseline for what is considered "classic" would certainly differ. It is common for such relative terms to find their way into flavor descriptions.
Often Haden is described as having a resinous character to the flavor, which indicates that there is a high concentration of certain flavor compounds.