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Wittgenstein is a Kantian philosopher as far as the structure of the Tractatus, as far as the last part (section 6 and comments) are concerned with: that I cannot speak about the subject in the limits of the world is a deeply kantian conclusion.

But Kant also consideres transcendental logic to be a doctrine, so I cannot see in which sense he "doesn't speak about the subject in the limits of the world", since Logic is a theory and therefore I'm allowed to speak about it.

Given the considerations below, and/or more suggestions, if any ->

In which sense Wittgenstein is to be considered a kantian thinker with regard to metaphysics?

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Wittgenstein's Tractatus is said to be Kantian because it shares an abstract theoretical structure which we identify as typically Kantian. Kant's metaphysics is based on broadly epistemological premises (the nature of experience, of concepts, of judgments, etc) rather than on properly metaphysical premises. Analogously, The Tractatus' metaphysics is based on linguistic premises (the nature of linguistic meaning) rather than on properly metaphysical premises.

Kant:

Now, if it appears that when, on the one hand, we assume that our cognition conforms to its objects as things in themselves, the unconditioned cannot be thought without contradiction, and that when, on the other hand, we assume that our representation of things as they are given to us, does not conform to these things as they are in themselves, but that these objects, as phenomena, conform to our mode of representation, the contradiction disappears. (Critique of Pure Reason Preface to 2nd edition)

Wittgenstein:

5.6 The limits of my language mean the limits of my world.
5.61 Logic pervades the world: the limits of the world are also its limits. So we cannot say in logic, ‘The world has this in it, and this, but not that.’ For that would appear to presuppose that we were excluding certain possibilities, and this cannot be the case, since it would require that logic should go beyond the limits of the world; for only in that way could it view those limits from the other side as well. We cannot think what we cannot think; so what we cannot think we cannot say either. (Tractatus)

Further, Kant argues about a barrier beyond which nothing can be known. Analogously, Wittgenstein argues about a barrier beyond which nothing can be said.

Kant:

We may look upon it as established that the unconditioned does not lie in things as we know them, or as they are given to us, but in things as they are in themselves, beyond the range of our cognition. (Critique of Pure Reason Preface to 2nd edition)

Wittgenstein:

5.62 This remark provides the key to the problem, how much truth there is in solipsism. For what the solipsist means is quite correct; only it cannot be said, but makes itself manifest. The world is my world: this is manifest in the fact that the limits of language (of that language which alone I understand) mean the limits of my world. (Tractatus)

P.S. Transcendental logic does not seem to be related here. Perhaps you are mixing transcendental (a property of inquiries) with transcendent (a property of things)?

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    I like the thoughts presented here, although I think concrete text-examples would improve this answer very much. But two points strike me: Transcendental as property of inquiries seems strange to me. It may be described (if simplified and no longer kantian in the full sense) as a method of inquiry, but a property? The same holds for transcendent as property of things, as things are usually thought to be/defined as epistemic entities, while transcendence is usually tied to concepts that...well...transcend knowledge.
    – Philip Klöcking ♦
    Mar 23, 2016 at 22:03
  • @PhilipKlöcking I've added some text excerpts, as you suggested. Thanks for the comment.
    – Ram Tobolski
    Mar 24, 2016 at 18:42

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