So to clarify, you asked why Jesus (as) and Adam (as) are considered to be the only two people who are said to have had the Spirit of God breathed into them. And you are wondering why is it that Jesus (as) has such a special status as to being called the Word of God and the Spirit of God. Correct?
To answer your question, consider that the Arabic for Word is "Kalimat" and Spirit is "Ruh". I won't write in Arabic letters because I don't know if you know how to read Arabic or not. My guess is that you read verse 4:171 in the Qur'an and you were wondering why this was said at all about him and no one else. The short answer is that he is not the only one to whom this kind of reference was given. I have seen translations say one thing and another in their English meaning, but when I read the Arabic, even by not knowing that much of it, I find that the term "Ruhun minhu" (Spirit from Him) is used elsewhere in the Qur'an as well.
This term is used in verse 58:22:
58:22 Thou wilt not find any people who believe in Allah and the Last Day, loving those who resist Allah and His Messenger, even though they were their fathers or their sons, or their brothers, or their kindred. For such He has written Faith in their hearts, and strengthened them with a spirit from Himself. And He will admit them to Gardens beneath which Rivers flow, to dwell therein (for ever). Allah will be well pleased with them, and they with Him. They are the Party of Allah. Truly it is the Party of Allah that will achieve Felicity.
Furthermore, that website you read on this issue about, which said that only Jesus (as) and Adam (as) are mentioned to have had a Spirit breathed into them by Allah from Himself in special mention is incorrect. In fact, Hazrat Bibi Maryam (ra) also had a special mention of this in the Qur'an as well:
21:91 And (remember) her who guarded her chastity: We breathed into her of Our spirit, and We made her and her son a sign for all peoples.
It doesn't say specifically "Ruhun minhu" here as well, but the meaning is all the same here. The point of this verse is to demonstrate to you that that website you went to was not accurate. If what you claim it said is true.
Another point to note is that after all of this it becomes clear that the Spirit which Allah gave from Himself does not form a part of His Divine Self, but it is only a gift of Allah to those whom He sees worthy of attaining this gift. The proof of this is that the term "minhu" (from Him) is used in this sense elsewhere in the Qur'an:
45:13 And He has subjected to you, as from Him, all that is in the heavens and on earth: Behold, in that are Signs indeed for those who reflect.
The Qur'an uses these expressions of "Kalimat" (Word) and "Ruh" (Spirit) because there were ugly charges made against him by the Jews against him and his mother. Thus, you can appreciate that the Holy Qur'an has cleared both Jesus (as) and Mary (ra) of these charges. Allah Himself said that their status was high and was not as the Jews said they were. This is a very high stance they have with Allah and it is a great mercy from Him. It also shows how much they were both insulted. Imagine how much the hearts of those Christians who heard this from such a huge group of Jews felt, especially the ones who were the target of this, Jesus (as) and his pure and noble mother, Mary (ra).
Furthermore, the mention of Jesus (as) being the "Word" of Allah, "Kalimat", is an interesting notion in the Qur'an. If I am correct, Christians (meaning you as well) generally believe that Jesus (as) is the Word of God personified. He is considered above all of the other Prophets, because none of them shared in this status (according to them) and thus he is superior and completely distinguishable from them. There is pride in his being this special "Word" of God because he shared in it eternally and was then human. Again, correct me if I am wrong. I am trying to paint the picture here of how highly Christians praise Jesus (as) with regard to this.
That being said, the Holy Qur'an has shattered this picture for the Christians. Allah has said in the Holy Qur'an:
18:109 Say: "If the ocean were ink (wherewith to write out) the words of my Lord, sooner would the ocean be exhausted than would the words of my Lord, even if we added another ocean like it, for its aid."
This verse is speaking about the "Kalimat" of Allah. Allah has an inexhaustible reserve of His Kalimat (Words) which nothing can satisfy.
This fact is further corroborated by the Holy Qur'an when it explains that Jesus (as) was only a humble Messenger of Allah and a human being like any other, despite his very high status with Allah in terms of his spiritual rank and closeness with Him:
43:59 He was no more than a servant: We granted Our favour to him, and We made him an example to the Children of Israel.
And in fact he, as well as the Holy Prophet (saw), were no more than servants of Allah:
19:30 He said: "I am indeed a servant of Allah: He hath given me revelation and made me a prophet;
And now to finally quote verse 4:171, we find that it says all of these things as well. Knowing what you know after all of this, you can read it and appreciate it in a different manner:
4:171 O People of the Book! Commit no excesses in your religion: Nor say of Allah aught but the truth. Christ Jesus the son of Mary was (no more than) a messenger of Allah, and His Word, which He bestowed on Mary, and a spirit proceeding from Him: so believe in Allah and His messengers. Say not "Trinity": desist: it will be better for you: for Allah is one Allah: Glory be to Him: (far exalted is He) above having a son. To Him belong all things in the heavens and on earth. And enough is Allah as a Disposer of affairs.
Thus, Jesus (as) was only a Messenger, and only His Word, and a Spirit, which was gifted from Allah to him. He was not part of a Trinity of Godhood, instead, he was what Allah said he is in this Ayat. His being a Word of Allah and a Spirit from Him does not mean he was specially above any of the other Prophets of Allah by being gifted divinity. Rather, he was like all of the rest of the Messengers of Allah. They had Allah's Words bestowed upon them, and they had been vested with the Spirit of Allah as well. "Ruh" itself has many different meanings, such as inspiration, revelation, mercy, soul or spirit, and breath which pervades the whole body after the exit of which man dies, angel, Qur'an, joy and happiness. So "Ruh" applies to many things and many people, and this would include all of the Prophets of Allah as well since they shared in the revelations as well.
Peace be upon those who seek the truth.