He has prescribed for you the religion which He enjoined upon Noah and which We revealed to you (O Muhammad), and which We enjoined upon Abraham and Moses and Jesus, commanding: “Establish this religion and do not split up regarding it.” What you are calling to is very hard upon those who associate others with Allah in His Divinity. Allah chooses for Himself whomsoever He pleases and guides to Himself whoever penitently turns to Him.
The above is the translation by Abu Ala Mawdudi from Taheem-ul-Qur'an, in explaining the word iqamat he further writes
The word iqamat (to establish) when used in respect of a material or physical object implies causing it to rise from the sitting or lying positions or assembling the scattered parts of a thing and raising it up high. But when iqamat is used in respect of a thing which is not material but spiritual in nature it does not merely imply preaching it, but also acting according to it as best as one can, introducing it and enforcing it practically. For example, when we say that so and-so established his rule, it does not mean that he invited others to his government but that he subdued the people of the land and organised the different departments of the government in a way that the administration of the country began to function according to his orders. Similarly, when we say that courts have been established in the country, it means that judges have been appointed to do justice and they ate hearing the cases and giving judgement, and not that hymns in praise of justice are being sung and the people being impressed.
Mawdudi, a very prominent scholar of 20th century is obviously of the opinion that it's the duty of every individual who calls himself a Muslim to strive for the establishment of Islam all over the world.
There was one criticism which came from Waheed Uddin Khan where he argued in his book Tabeer ki Ghalti that Religion here doesn't include Sharia since the verse is talking about Religion given to all the Previous Prophets and we know from Qur'an that different Sharia was given to different prophets. Mawdudi gave a counter argument to this in his tafseer
When some people saw that the din which has been enjoined to be established is common among all the Prophets, and their shari'ahs have been different, as Allah Himself says: "We appointed for each community among you a law and a way of life", they formed the view that inevitably this din did not imply the shari' ah commandments, rules and regulations but only the acceptance of Tauhid, the Hereafter and the Book and the Prophethood and performance of certain acts of devotion to Allah, or at the most, it included some of the major moral principles which have been common to all the shari'ahs. But this is a superficial view, which has been formed after having a cursory glance over the unity of religion and the difference of the shari'ahs. This is, however, a dangerous view, which if not corrected in time, may well lead to the separation between din (religion) and shari'ahs (law). It was this very view in, which St. Paul was involved, who presented the doctrine of the din (religion) without shari'ah (law), and corrupted the community of the Prophet Jesus (peace be upon him). For, if shari'ah (law) is something separate from din (religion) and the command is only for establishing the din and not the shari'ah, inevitably the Muslims also, like the Christians, would regard the shari ah as unimportant and overlook its establishment as not being the real object by itself, and would remain content with only beliefs and a few important moral principles. Instead of determining the meaning of din from such speculations, let us turn to the Qur'an itself and see whether the din which we have been enjoined here to establish implies the beliefs and a few important moral principles only, or the shari'ah values and commandments as well
He then cites verses where deen is used as a synonym for sharia example: 5:3 and 9:29.
So with this background if one claims that it's the religious duty of every Muslim to strive for the establishment of Islam all over the world, isn't he right?