In short, no, these verses aren't meant for all of mankind because the instructions here are meant for Muslims only. All of mankind isn't saved from the brink of fire, and neither is there ever going to be a collective effort for mankind to make a group of people preach the message of Islam as their life mission. It would be contradictory since then in that case all of mankind would have been guided.
As for the teaching Jesus (as) made about neighbors, Islam has laid a similar emphasis on neighborly love:
Narrated 'Aisha: The Prophet said "Gabriel continued to recommend me about treating the
neighbors Kindly and politely so much so that I thought he would order me to make them as my heirs. (Book #73, Hadith #43)
(Sahih Bukhari)
Narrated Abu Shuraih: The Prophet said, "By Allah, he does not believe! By Allah, he does not believe! By Allah, he does not believe!" It was said, "Who is that, O Allah's Apostle?" He said, "That person whose
neighbor does not feel safe from his evil." (Book #73, Hadith #45)
(Sahih Bukhari)
Narrated Abu Huraira: Allah's Apostle said, "Anybody who believes in Allah and the Last Day should not harm his
neighbor, and anybody who believes in Allah and the Last Day should entertain his guest generously and anybody who believes in Allah and the Last Day should talk what is good or keep quiet. (i.e. abstain from all kinds of evil and dirty talk). (Book #73, Hadith #47)
(Sahih Bukhari)
Narrated 'Aisha: I said, "O Allah's Apostle! I have two
neighbors! To whom shall I send my gifts?" He said, "To the one whose gate in nearer to you." (Book #73, Hadith #49)
(Sahih Bukhari)
Narrated Aisha: I said, "O Allah's Apostle! I have two
neighbors and would like to know to which of them I should give presents." He replied, "To the one whose door is nearer to you." (Book #35, Hadith #460)
(Sahih Bukhari)
It is arrested on the authority of Anas b. Malik that the Prophet (may peace and blessings be upon him) observed: one amongst you believes (truly) till one likes for his brother or for his
neighbour that which he loves for himself. (Book #001, Hadith #0072)
(Sahih Muslim)
It is narrated on the authority of Abu Huraira that the Messenger of Allah (may peace and blessing be upon him) observed: He will not enter Paradise whose
neighbour is not secure from his wrongful conduct. (Book#001, Hadith #0074)
(Sahih Muslim)
Abu Huraira reported Allah's Messenger (may peace be upon him) as saying: 0 Muslim women, none of you should consider even a sheep's trotter too insignificant to give to her
neighbour. (Book #005, Hadith #2247)
(Sahih Muslim)
Abu Dharr reported Allah's Messenger (may peace be upon him) commanded me thus: Whenever you prepare a broth, add water to it, and have in your mind the members of the household of your
neighbours and then give them out of this with courtesy. (Book #032, Hadith #6358)
(Sahih Muslim)
The companions of the Holy Prophet (saw) were very serious in following all of his injunctions. Here is another version of one of the narrations I gave above:
Abu Huraira (Allah be pleased with him) reported Allah's Messenger (may peace be upon him) as saying: None among you should prevent his
neighbour from fixing a beam in his wall. Abu Huraira (Allah be pleased with him) then said: What is this that I see you evading (this injunction of the Holy Prophet)? By Allah, I will certainly throw it between your shoulders (narrate this to you.) (Book #010, Hadith #3918)
(Sahih Muslim)
So there is a lot of stress on good relations with neighbors in Islam. I don't know of any verses of the Qur'an on neighborly relations, but there is a lot of emphasis by the Holy Prophet (saw) on being good towards neighbors. There is no distinction of neighbors in terms of being Muslim or non-Muslim. All are to be treated well.