I'm not a physical chemist, but I would say alloys ARE mixtures. Your definition says it clearly: in a mixture the components keep their properties. If they don't, it's not a mixture.
I quote myself because I wrote it wrong: I meant 'I would say alloys AREN'T mixtures'. Sorry. Besides, the rest of my reasoning was conflicting with the statement that alloys were mixtures.
However, I see this has raised quite a lot of comments and different opinions, and I still wouldn't be sure of the answer.
The two metals in an alloy DO lose their identity in some cases. Brass (Zn+Cu) is not attacked by dilute mineral acids, whereas pure Zn is. If it was a mechanical mixture, as finely divided as you want, the acid would still be able to go and dissolve the Zn crystals.
Yet in other cases it doesn't happen. For instance, if I remember well, the preparation of Raney Nickel involves treating a Ni-Al alloy with aqueous NaOH. Al is dissolved by NaOH, leaving a microporous Ni.
I'm not entirely convinced by Borek's reply, i.e. that you can separate the metals by distilling the alloy, hence it's a mixture. As it was said before, the metallic bond is different from covalent bonds, so I wouldn't be sure that the energy you supply for the distillation isn't actually breaking the bonds instead of just breaking the interactions between individual, discrete metal particles.
In fact there are countless organic compounds that decompose if distilled at atmospheric pressure, because they have a covalent bond which is weak enough to be broken by the available thermal energy.
Finding two different substances in the distillate fractions wouldn't make you conclude that the starting material is a mixture, would it?
But still, I may be wrong...