I think that any comprehensive account of meaning must include an account of intentionality, but the real challenge is to give an account of both meaning and intentionality in non-intentional terms. Otherwise, we risk spinning in a little circle. Here is Brandom in Between Saying and Doing:
"If one is allowed to use the full resources of semantic vocabulary in specifying the use—describing an operator as ‘used so as to express negation’, or a term as ‘used to refer to Leibniz’, then the semantic pragmatist’s claim that use confers meaning (so talk of practices or the exercise of abilities as deploying vocabularies) reverts to triviality if we are allowed to talk about “using the tilde to express negation”, “the ability to mean red by the word ‘red’”, or “the capacity to refer to electrons by the word ‘electron’,” (or, I think, even intentions so to refer)".
What stands in the way of giving up intentionality is a very strong intuitive conviction that "any given word" is "meaningful/significant in the first place", that it has some in-dwelling meaning onto itself, which governs its use. Many now see it as one of the forms of the Myth of the Given, and 20th century developments in epistemology undermined this conviction significantly. The counterarguments include not only Sellars's and Adorno's against it specifically, but also Quine-Davidson's indeterminacy of interpretation, Wittgenstein's rule-following indeterminacy, etc. Basically, epistemological theories of such in-dwelling meaning, both phenomenological a la Husserl and empirical, face severe difficulties in accounting for its learnability and communicability, and in a more practical vein they lead to the frame problem in AI research, see How can one refute John Searle's "syntax is not semantics" argument against strong AI?
If the inferentialists are right then our "intentional acts" amount to mastering inferential roles, and ultimately habits of use, and the order of explanation reverses: words are not meaningful in themselves, and there is no need to explain how they can be so. The in-dwelling meaning is a confabulation many ages in developing, a stand-in for certain ingrained activities or their parts. Sellars gives a hypothetical reconstruction, the Myth of Jones, of how our intentional talk might have developed historically. Dreyfus describes Merleau-Ponty's non-representational account of intentionality as a solution to the frame problem in Why Heideggerian AI Failed:
"According to Merleau-Ponty, as an agent acquires skills, those skills are “stored”, not as representations in the mind, but as a bodily readiness to respond to the solicitations of situations in the world. What the learner acquires through experience is not represented at all but is presented to the learner as more and more finely discriminated situations..."
This raises several concerns. First, if we are excluding intentional vocabulary then the only alternative seems to be purely functionalist or behaviorist causal description, and it seems unlikely that intentionality can be conjured out of that. This is often raised in the context of the mind-body problem. Brandom himself insists that his pragmatics is normative, and this normativity cannot be reduced to naturalistically describable regularity of behavior. Second, to describe an activity we need to specify what it is applied to and how it proceeds, which itself requires using representational language. And finally, if everything reduces to our activities then where in all of this does reality get its say in influencing our meanings? This is McDowell's problem of "objective purport", ignoring which perennially leads to the oscillation between naive sense empiricism and coherentism, in his view, see How is the conflict between created by reason and external aspects of knowledge resolved?
These are thorny issues. While intentional semantics may look unpromising, semantic inferentialism, or other alternatives, may not have an adequate language either, at least not yet. The situation is reminiscent of the one in physics in 1910s. There were well established phenomena where light behaved like waves, and newly discovered ones, where it behaved like particle beams. Old quantum mechanics focused on the latter, but it could not answer if we can have optics without waves altogether. Not until it developed new vocabulary and framework, compared to which wave talk, particle talk, and even "complementarity" talk, were deficient. I think Nagel is on the right track when he writes in What is It like to be a Bat?
"So if our idea of the physical ever expands to include mental phenomena, it will have to assign them an objective character... It seems to me more likely, however, that mental-physical relations will eventually be expressed in a theory whose fundamental terms cannot be placed clearly in either category."
As Bohr emphasized, application of quantum mechanics must always involve classical apparatus and measurements, but quantum language remains primary in the order of explanation. So invoking representational language to describe activities does not threaten their primacy. And if the dichotomy between intentionality and causalism is a false dichotomy, then we can start to see how the relation between us and reality can be justificatory, and not merely causal, without succumbing to the Myth of the Given. "Habits", "norms", "commitments and entitlements" are perhaps the seeds of a new vocabulary, which will be neither mentalistic, nor naturalistic.