The two references from the Watchtower Online Library you partially quote both mean that Jehovah’s Witnesses believed that October 1914 marked the end of the Gentile Times. The expression “the appointed times of the nations” means that the time during which God would allow the Gentile nations free reign, would come to a dramatic end with the battle of Armageddon. They claimed that in October 1914 Jesus took up his heavenly kingdom and began ruling, invisibly, from heaven. However, this is what they believed before 1914 and right up till 1930:
"But bear in mind that the end of 1914 is not the date for the beginning, but for the end of the time of trouble. Zion's Watch Tower 1894 July 15 p.226
"The year A.D. 1878 … clearly marks the time for the actual assuming of power as King of kings, by our present, spiritual, invisible Lord…" The Time is At Hand (1911 edition) p.239
"… from the beginning of the Lord’s presence in 1874 the Devil used the Papal system as the chief opposing instrument of God’s kingdom …" Watch Tower 1930 September 15 p.275
Those beliefs had to be changed after nothing happened in October 1914:
"The Watchtower has consistently presented evidence to honest-hearted students of Bible prophecy that Jesus’ presence in heavenly Kingdom power began in 1914." Watchtower 1993 January 15 p.5
"Jehovah's witnesses pointed to the year 1914, decades in advance, as marking the start of "the conclusion of the system of things." Awake! 1973 January 22 p.8
It wasn’t until 1943 that the book "The Truth Shall Make You Free" moved forward the end of six thousand years of man's existence into the decade of the 1970's thereby eliminating the year 1874 as the date of return of the Lord Jesus Christ and the beginning of his invisible presence or parousia. On page 324 it says: "The King's presence or parousia began in 1914."
Also, the belief that the “Gentile Times” had ended in 1914 has had to be changed because it’s over 100 years since Jesus supposedly started ruling, invisibly, from heaven and Armageddon is still some time future.
Baptist William Miller came up with calculations pointing to 1844 as the second coming of Christ Jesus. Seventh Day Adventists, along with members of the Bahai’ Faith, also point to October 1844 as being highly significant with regard to end-time prophecy. As far as I am aware, the only other group apart from Jehovah’s Witnesses who still cling to 1914 are the survivors of the original Bible Students who voted with their feet and left the organisation after the second President, Rutherford, introduced the name Jehovah’s Witnesses.
EDIT: Here is the quotation that led me to think the Society had changed its view about the Gentile Times ending in 1914 followed by more recent (2014) information on the subject:
Furthermore, the remnant of spiritual Israel had for decades, yes, since 1876, been looking forward to the ending of the Times of the Gentiles in the autumn of 1914...  marked the beginning of a period of education in the written Word of God from the standpoint that Bible prophecy is best understood after it has been fulfilled. So there needed to be a correction of our previous views, and the surviving remnant of spiritual Israel needed to be readjusted to the post-war realities and opportunities. ... This revised program of Bible education had a profound effect on the remnant. It oriented their work in the right direction. (Man's Salvation Out Of World Distress At Hand; 1975; p. 191 and 136)
On the morning of Friday, 2 October 1914, C.T. Russell came to breakfast at the Brooklyn Bethel HQ and announced “The Gentile Times have ended; their kings have had their day!” (God’s Kingdom Rules, published 2014, page 2) That publication goes on to explain why the eagerly anticipated events surrounding the end of the Gentile Times in 1914 did not take place and that Jesus, as Judge of all the nations will also become the Executioner of nations – but not until the Great Tribulation culminates in the battle of Armageddon. (God’s Kingdom Rules, published 2014, page 228)
The meaning assigned to the phrase, the “end of the Gentile Times” (or “the appointed times of the nations”) no longer means the actual end of rulership by human governments but now means the end of their uninterrupted rule of the earth. This is because Jehovah’s Witnesses believe that Jesus began ruling (invisibly) from heaven in October 1914. The new understanding (as best I can make of it) is that the rulers of the nations are now on “borrowed time” because although their time ended in 1914 the Great Tribulation and Armageddon are still some time future.