What do you mean by intelligent? Different people have different talents, do you call a writer's ability to create a creative story as intelligent? Or a scientist who invent something new?
Different people are more sensitive to different things, but there are too mamy kinds of things, so we can't measure it.
Well by your own example : if someone has MORE of these and more talents than someone else it's fair to say they are more intelligent no?
Your argument breakdown in its very premise. That's like saying that because there are different types of water water can't be defined. That's silly.
In general intelligence seem linked with abilities that made civilizations develop their infrastructure, create the kind of complex cooperative structures allowing for - for example - western civilization. Basically the reason why you're not living in a cave trading your iphone for banging rocks together.
There's plenty of research on the topic, and I don't think it would be useful to call any trait you'd like 'intelligent'. Yes we can but then it just becomes meaningless.
A good dancer is not 'intelligent' he/she is a good dancer. We already have categories for that and people tend to intuitively agree on what constitutes intelligence.
We are not all equal at all things, saying someone can be better at x or y or z than another person and that we have 'many talents' doesn't contradict it.
There are exceptions of course, but overall more intelligent people are rarely just good at 'one thing' - we are not talking about Hollywood-movie-like clichés. Intelligent people tend to be better than average at a vast majority of cognitive tasks/skills not just say 'be good at math'. Someone who's simply very good at one thing would be - for example - a 'savant' but these are abnormalities and not the rule.
Aboriginal Australians for example are better than westerners at navigating in the Australian plains - finding a spot and their ways home and have excellent spatial memory. However would you call them 'more intelligent' just because of that despite the fact that they never managed to invent the bow and are , overall, utterly failing at navigating the landscapes of modern civilizations despite billions invested in uplifting them? I wouldn't.
In the case of IQ for example someone with a high performance IQ means they are better and faster than average at a multitude of types of cognitive tasks, it usually also comes together with a high verbal IQ (so language proficiency, a more varied lexicon and better general comprehension etc.), more ease at grasping concepts, greater neural activation patterns (so to simplify, more complex thought), accelerated learning curve, and a plethora of other things. IQ has also been correlated with the success of nations with a far greater success at applying western type technological civilization in countries with a population at similar or superior IQ levels than in the western world (East Asia for example) etc etc etc.
Would I call western-type civilizations superior to say hunter gatherer societies? Absolutely.