The section of the Westminster Confession you have quoted, Chapter I, section VII, explains how there is no limiting factor within the scripture, regarding those things necessary for salvation, which gives advantage to the learned over the unlearned.
Just prior to that Chapter 1 Section VI reads (in part):
The whole counsel of God concerning all things necessary for His own glory, man’s salvation, faith, and life, is either expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture: unto which nothing at any time is to be added, whether by new revelations of the Spirit, or traditions of men.(m) Nevertheless we acknowledge the inward illumination of the Spirit of God to be necessary for the saving understanding of such things as are revealed in the Word
And again in Section X:
The supreme judge by which all controversies of religion are to be determined, and all decrees of councils, opinions of ancient writers, doctrines of men, and private spirits, are to be examined; and in whose sentence we are to rest; can be no other but the Holy Spirit speaking in the Scripture.
In short the spiritual truths necessarily relating to our salvation are spiritual truths recorded in a physical media and are thus to be discerned in both ways. The natural man cannot, by nature alone, apprehend the things of the Spirit:
Now we have received not the spirit of the world, but the Spirit who is from God, that we might understand the things freely given us by God. And we impart this in words not taught by human wisdom but taught by the Spirit, interpreting spiritual truths to those who are spiritual. The natural person does not accept the things of the Spirit of God, for they are folly to him, and he is not able to understand them because they are spiritually discerned. - 1 Cor 2:12-14
For one example, Peter confessed Jesus to be the Son of the Living God and Jesus declared that Peter did not come by that knowledge through flesh and blood. Another example is Nicodemus' complete ignorance regarding the new birth even though he was 'the' teacher of Israel.
Trinitarian belief is necessary for salvation (according to Trinitarians) for two major reasons outlined in the confession:
- Chapter VII, section 1 - The gulf between Holy God and creature is so unbridgeable and immense to man that reconciliation must be an act of God:
The distance between God and the creature is so great, that although
reasonable creatures do owe obedience unto Him as their Creator, yet
they could never have any fruition of Him as their blessedness and
reward, but by some voluntary condescension on God’s part, which He
hath been pleased to express by way of covenant.
- Chapter VIII, section II - Jesus Christ is that voluntary condescension of God, taking upon Himself the nature of a created being to accomplish as a man and for mankind, what man is utterly incapable of doing:
The Son of God, the second person in the Trinity, being very and eternal God, of one substance and equal with the Father, did, when the fulness of time was come, take upon Him man’s nature, with all the essential properties and common infirmities thereof, yet without sin: being conceived by the power of the Holy Ghost, in the womb of the virgin Mary, of her substance. So that two whole, perfect, and distinct natures, the Godhead and the manhood, were inseparably joined together in one person, without conversion, composition, or confusion. Which person is very God, and very man, yet one Christ, the only Mediator between God and man.
The Holy Spirit is said to be eternally proceeding from the Father and the Son in Chapter II, section III:
In the unity of the Godhead there be three persons, of one substance, power, and eternity; God the Father, God the Son, and God the Holy Ghost. The Father is of none, neither begotten, nor proceeding: the Son is eternally begotten of the Father: the Holy Ghost eternally proceeding from the Father and the Son.
This is that Spirit that searches all things, even the deep things of God; who has been sent into the world to convince the world of sin and of righteousness and of judgement; severally referred to as the Spirit of God, the Spirit from God, the Spirit of Truth, and the Spirit of Christ and who dwelt in the flesh of Jesus without measure. This same Spirit was present and active in creation, inspired and illuminates Scripture to human hearts, regenerates and adopts the lost, lives and strives within the redeemed to produce conformity to Christ, and guarantees the inheritance. It is the same eternal Spirit by which Christ offered Himself without blemish to God on our behalf and who Jesus promised to send to be with us and in us forever.
Simply put Trinitarians are convinced from Scripture by natural apprehension and spiritual illumination of what is written that a Jesus who is not the only begotten Son of God, the Logos who was God in the beginning and never ceased to be God during the incarnation, is not capable of providing salvation to all mankind because the chasm between God and Man is uncrossable to Man. Therefore trinitarian belief is considered necessary for salvation because a merely human Jesus cannot save and man, unaided by the Holy Spirit, cannot apprehend salvation.
This is not to say that full doctrinal understanding is necessary in advance. Indeed, all (in whatever condition they currently exist) who call upon the name of the Lord will be saved. Following the new birth, however, the Holy Spirit will never illuminate scripture and enable understanding of that which is untrue. A saved individual, then, who from a sincere heart desires to grow in the grace and knowledge of the Lord Jesus Christ can reasonably expect, over time through prayer, study, and a heart of obedience, to increase in apprehension of the Triune God.