An essential feature of abstract things is that they do not exist independently and in their own right. For example,
this chair or
that man (whose name is John) are concrete objects. However, the concepts "chair" and "man" are abstract. They do not exist in themselves as such. The same can be said for something like "brown", an attribute that, let's say, is instantiated by both the chair and by John in some way, but which cannot exist by itself as such. So we can say that "chair", "man" and "brown" all exist "in" these concrete things (or more precisely, determine these things to be those things or in those ways). However, apart from those things that instantiate them, these forms also exist somewhere else, namely, the intellect. However, they exist in our intellects without instantiating them. Otherwise, we would literally have to have a chair or a man or something brown in our intellects the moment we thought these things. So you have a problem. You have a kind of substratum in which these forms can exist without being those things. That does not sound like matter because when those forms exist in matter, they always exist as concrete instantiations of those things.
W.r.t. derived intentionality, the relation that obtains here between a signifier and the signified is in the mind of the observer. When you read "banana", you know what I mean because the concept, in all its intrinstic intentionality and semantic content, already exists in your intellect and you have learned that that string of symbols is meant to refer to that concept. I could, however, take a non-English speaker and mischievously teach them that "banana" refers to what you and I would use the term "apple" to mean. No intrinsic relation exists between the signifier and the concept. However, there is an intrinsic relation that obtains between concepts and their instantiations. The concept "banana" is what it means to be a banana. So the derived intention involves two relations, namely, one between the signifier and the concept (which is a matter of arbitrary convention) and another relation between the concept and the signified, which necessarily obtains between the two. Derived intentionality is parasitic on intrinsic intentionality. The former requires the latter.
So what is meant when we say that computers do not possess concepts (i.e., abstract things), only derived intentionality, we mean that computers are, for all intents and purposes, syntactic machines composed of symbols and symbol manipulation rules (I would go further and say that what that describes are really abstract computing models like Turing machines, whereas physical computers are merely used to simulate these abstract machines).
Now, my whole point earlier was that if we presuppose a materialist metaphysical account of matter, we will be unable to account for intrinsic intentionality. This is a well known problem. And if we cannot account for intrinstic intentionality, then we certainly cannot make sense of derived intentionality.