I am quite aware that the solipsism professed in the Tractatus is not of narcissistic of vain attitude. Rather Wittgenstein, from my readings, professed an attitude of humility and selflessness (mentioned in the OP) by professing solipsism.

Here is the part that directly addresses the OP's question. Anyone care to help me unpack it?

This leads us to the final solipsistic doctrine of the Tractatus. 'Solipsism, when its implications are followed out strictly, coincides with pure realism. The self of solipsism shrinks to a point without extension and there remains the reality coordinated with it' (TLP, 5.64). Wittgenstein's doctrines have of course followed out the implications of solipsism. How do they show that solipsism, paradoxically, coincides with pure realism? The analysis of propositions about other minds willnot mention the metaphysical self, or a Cartesian res cogitans. It is plausible to think that such propositions will be analysed in some way or other in terms of names referring to elements of my experien~e.~~ Hence if epistemological realism is, roughly speaking, the commonsense view of the world expressed in propositions such as 'A has toothache', 'The is shedding its leaves', then transcendental solipsism does not deny that such propositions are sometimes true. Nor indeed does it claim that 'I am the only person who exists' is true. What it claims is that the analysis of such propositions into elementary propositions is to be carried out in a certain way. The truth of solipsism will manifest itself in the fact that the analysis of 'I have toothache' will differ in important ways from the analysis of 'A has toothache' (where A is not myself). The former will involve reference to the experience of toothache. The latter will refer only to the behaviour which others manifest when they are said to have toothache. But even in the analysis of 'I have toothache' the metaphysical self, the self of solipsism, will not appear. It will be the constant form of all experience, presumably represented in the ideal notation by the variable or variables taking names of unanalysable elements of experience or perhaps names of objects in general as values. Thus everything the realist wishes to say can be said; and nothing the transcendental solipsist wishes to say can he spoken of. There will be no practical disagreement between them, nor will they quarrel over the truth-values of propositions of ordinary language. But the analysis of such propositions will manifest the transcendental truths that cannot he said. Wittgenstein's doctrine in the Tractatus is best described as Empirical Realism and Transcendental Solipsism.

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