The question about possible types of intelligence is ridiculously complex, partly/fully philosophical, and way beyond the scope of a question or an answer thereof. We are also fundamentally quite limited in trying to think of possible ways to think, our approaches in artificial intelligence, for example, are merely trying to replicate the human way of thinking and seeing the world.
When it comes to a creature that has to combat members of the same species for all possible resources, it probably has developed physical characteristics suitable for it. They might be very fast and agile in order to make surprise attacks, or very strong, bulky and well protected to resist the attacks of others and slug the opponents with heavy blows.
All this is rather irrelevant to your question, as for the intelligence capabilities: your creature is probably quite stupid. Fighting is essentially very easy, and if you know you are going to fight for everything anyway, there is no need to develop intelligence. We, homo sapiens, are so "smart" because we had to become flexible, cunning and outsmart the opponent. Originally, some time ago though, we were actually prey to many animals. So at the same time, we had to develop skills to hide from a predator, but be an efficient predator at the same time. Simultaneously, we had to develop skills find food from bushes and trees; roots and fruits. These skills are more or less mutually exclusive, so acquiring them "increased" our capabilities. If there was only one way to find food, shelter and mating partner, namely fighting, we would have just become big, strong, stupid apes.
Another part of becoming smart, at least the way we know it, is to grow large brains. For a fighter, this has multiple problems. The brain is very fragile and would require protection in a fight, and would certainly be a target to the opponent. Secondly, big thinking power requires a lot of energy. A creature that spends most of its energy to fight for resources, would not have this surplus to grow big thinking organs. Lastly, at least in our understanding of intelligence, a big brain is not enough, but you need to train it (slowly learning things). This would mean that young baby creatures would have to take time learning from their "parents", which would, of course, be impossible if fights would occur constantly.