I’m not sure what you mean by “along something”? Do you just mean a standard by which to measure?

If you just mean that there needs to be a way of determining, in some cases, that one thing is “more intelligent” than another, then yes, that is necessary for “intelligence” to be a useful notion.

But we do have methods of doing that, so there is no problem there.

Note that the way we have of comparing intelligence needn’t be a linear order. It can be a partial order.

I agree, it's multidimensional.

If "general" truly meant general purpose, the measure might be how well the system arranges every possible (sequence of) combination(s) of matter and energy in space and time, while optimizing along any combination of these.

But that in itself is not a single objective, but a set of objectives, and not really a utility function.