The resistance value for the rheostat that you linked is acceptable however the wattage it can handle means it's probably a quiet a bit larger so keep that in mind, this isn't important except for size/weight. There's no way to tell from the markings on the POT what its wattage is unless it's written there plainly, but I somehow doubt the one you had was rated for 10watts, maybe 1, again that's just a rough guess. A big problem is that the rheostat you picked is a wirewound one, that adds a lot of inductance, and I don't know the construction of the one you linked but it doesn't look like any wirewound POT I've seen, so the inductance the one you picked may make the circuit work in unpredictable ways. You might want to post an image of that other side of the pot, and if you KNOW that it's bad and need to replace it possible use plyers to take it apart to look at it's internals, that will nail down exactly what it is.
A photo of the other side of the pot would help in identification or at least suggestions for a possible replacement. Is this pot that you have known to be bad? It seems solid and no burnt or what not. What's your reason for replacing it?