In case of elements it will work, but equivalents can be defined for compounds too. They are used quite often in analytical chemistry. In acid/base reactions equivalents are depending on the number of protons (so in case of monoprotic acid 1 equivalent = 1 mol, but in case of diprotic acid 1 equivalent = 1/2 mol), in redox reactions equivalent mass depends on molar mass and number of electrons exchanged and so on.
Definition you are talking about seems very limited to me.