The president is mostly a mediator, a role intended to avoid a failure along to the first republican system. The First Republic was almost fully parliamentary, and is remembered for its immense instability - over 40 governments in the course of 16 years. Thus came the necessity for a president.

Other than that, the fact that the parliament has so much power has to do with democratic values, especially relevant after the fall of a 48-year long fascist-like dictatorship.

So, to conclude, the president is a mediating figure the purpose of which is to avoid instability and to protect the values of the constitution (although this role belongs mostly to the constitutional court).

I'm not sure why you're unsure of it's dominance, both France and Germany showcased two models of it, as well as Austria Finland Italy turkey and a wave of former colonies who saw it as a functional balance between parliamentary instability and presidential potential for a takeover by the executive. Main development of constitutional law in the last century, with the advance of Kelsen's judiciary concepts as well.

In order to truly know the Portuguese political system, you need to have in mind the evolution of the country since 1910.Although Portugal had a constitutional monarchy since 1820, it was only with the republican revolution (October 5th of 1910) that were put down the foundations to the actual semi-presidential system of government.

The First Republic and the constitution adopted in 1911 stated that, although there would be a President, he didn’t had any type of right regarding the promulgation of the lawns from the senate or the government and that he himself could be destitute if the majority of the members of both cameras agreed. (aka a parliamentary system) A world war and a very unstable country to rule later, by December 5th of 1917 there is a military coup that overthrows the republic and implement a military dictatorship that decides, by decree in 1918, that the type of regime should be a presidential system. But again, with the assassination of the Sidónio Pais, the country enters in a time of government turmoil that only ends with another military coup in 1926 that would last until the carnation revolution, in April 25th of 1974. In the beginning of the dictatorship, although the constitution 1911 were still effective, it was only because there were no attempts to write another one. Advancing to 1933, the year that was implement the “Estado Novo” ruled by Salazar, the constitution stated that although there would be a President and a Council President (Salazar was never considered prime-minister, only a minister with power to rule the government and the country) the power belonged to the parliament. After a couple of constitutional revisions, that would be erase so that the power would belong solely to Salazar. Advancing again to the carnation revolution, the problem again arose: what type of system is the best for the new republic? It was obvious that the whole power couldn’t belong to a single person, it was one of the reasons for the revolution! But again, rely only on a parliament system was dangerous because of the turmoil observed in the first republic. So it was decided that both systems should be merged to provide the best support to the new democracy, with an emphasis in the parliament system. Even in the website of the President it is stated that “is role is much close to one of moderation between the different branches of the political system” although “still having the means to return the institution to their normal ways of operation”.

Tl;dr: After a couple of revolutions, insecurities and a long dictatorship, it was decided that there was a need to have a President and a Prime-minister so that both would control each other and so give the republican system it’s best qualities to survive.

Sources (all in Portuguese, my native language):

Parliament: historic notes

Presidency of the Portuguese Republic /

“O Semipresidencialismo no Portugal Democrático – Um estudo Longitudinal” by Carlos Lindo, revised by Prof. Doctor. Maria de Conceição Teixeira

Portuguese Constitution

NOTE: First time poster, any mistake/rule broken I appreciate the warning EDIT: Format