Eh, the last time this exact same W-I was posed, it got some quite definite responses about the hypothetical ancient Queen greatly influencing British cabinet policy, greatly influencing the Kaiser, plus there were a couple of handwave mini-TLs about dramatic things happening in areas outside the permit of any Victoria-related govt system.
This time, I have to admit, I do like the sound of this idea that even if her continued existence does somehow prevent 1914, then at least the great powers stil go to hell in a handbasket in 1919.
I thought I had seen this before

Glad I'm not going mad ... or madder then I already am lol
Is the significance here that she reigns through World War I, and her impact as a national icon during that conflict?
Otherwise, I'm not sure what effect there would be on her living to 100, since she was a figurehead, with little or no influence on policy.
WWI will not happen in Victoria's life time, no one will declare war on her in fear of being attacked by her grandchildren and none of the grandchildren will attack poor old nanny of Great Britain
Victoria will outlive her eldest son, Edward, making
Arthur heir to the British throne. If his son's stomach cancer is not butterflied away,
Princess Patricia will become King Arthur's heir apparent. Patricia is known for her intense dislike of British court life and decision to marry a commoner, which forced her to relinquish all titles.
Why has it jumped away from Prince Edward to Prince Arthur, when Prince Edward already had a son, Prince George? It would be like Prince Charles dying and then Queen Elizabeth II but instead of Prince William getting the Throne, Prince Andrew gets the job
But if Prince Arthur, was to be made King, I personally believe he, would use the regal name of William as no monarch of Britain would dare be called "King Arthur" lol. If his son still develops cancer, which is plausable, cancer doesn't stop if your heir to the Throne, look at poor Kiaser Frederick III of Germany. In this case his son Prince Alistar would be crowned and not be drunk in the snow dying of nuemonia in the snow, if he does die still at 28, would be succeeded by his cousin, Alexander Mountbatten.
Grandson Willy might just get a rather nasty telegram before the start of the war telling him he better calm down. IIRC I read something that she was one of the few people that he would obey with out any reservations.
Victoria wouldn't send a nasty telegram to Grandson Willy, it would be a polite little telegram from nanny britain, saying, she does not want him hanging around those naughty Hasburg kids getting into trouble - Followed by a new wooly jumper for winter
I could see that happening. Pope Pius X may not have been able to prevent World War I, but I think the "Grandmother of Europe" might have a fair shot.
Fair shot, she wouldnt even need to say a thing, no one will fight while nanny britain is alive.
I have this little cartoon of this old lady sitting at the head of the table talking nicely with the children, who are all being polite and smiling at one another but under the table they are kicking one another with out the old lady realising.
It ends with the old lady dying head first into the soup, with the children jumping at each other too quickly to realise they have lost Nanny

until its too late
I think a fascinating thing is that this could open up a World War after Victoria's death which has the same problems of outdated military methods with advanced weaponry, except with even more outdated military methods with even more advanced weaponry (depending on how military thinking and training evolves and develops in the lead up).
A World War in 1920, when every one is already on tender hooks, this will be a long and bloody war.
So if we're playing with the idea that a centenarian Victoria was able to stop (or at least delay) WWI, then we are looking at a Europe that is still a mish-mash of military alliances.
Why would they be mish-mash over 20 years of diplomatic talks alliance and trade partners could be changed.
Will Victoria still have influence over her Prime ministers?
HOWEVER, the multi-ethnic and unstable Austro-Hungarian Empire would have been forced to deal with the fact that it's current form was unviable and if it wouldn't engage in reform. It would face revolution.
Most likely, after all the A-H Empire was a fossil of the state in 1914, what will 6 more years of stagnant plodding along do to it, it may ever reform itself to allow devolution in Serbia, resulting in the War being avoided.
Russia in the meanwhile went through the February Revolution, and with Lenin stuck in exile the 'October' Revolution failed. But the attempts at creating a republic went nowhere and Michael wouldn't accept the throne under any circumstances. So Victoria along with the rest of Europe convinced the Russian government to ignore Nicholas's abdication decree barring his son from the succession and place Alexei Romanov on the throne as Alexander IV.
Will a revolution happen without WWI? Would Victoria not open her home to her grand-daughter, her grand-son-in-law the Tsar and her Great-grandchildren?
A marriage was arranged for him with a British Princess/Noblewoman and she bore him a son named Viktor that didn't have hemophilia.
Unlikely as Alexander is already a carrier, so all monarchs of russia will sadly be affected by hemophilia until it is watered down years from 1920.
I'm not sure if anything would change for the likes of Italy or Spain (still in it's Civil War), but the United States would be very much a quiet Great Power, a slumbering eagle just waiting for someone to wake it up...
I always forget about America, if WWI is advoided it would have a lot less influence of Europe then it has had in the past - and no lady liberty.
I also see Victoria absolutely insisting on giving refuge to the Romanov's if they fall from power in Russia.
Another thing that intrigues me, though I don't know if her influence is this profound, but would she prevent Britain's Entente Cordiale with France in 1904? I ask only because it seems to me that event was a very large break with historic British policy of remaining neutral on the continent. Without a formal Entente, a firm declaration from Britain that she will guarantee the independence of Belgium against any power (aka Gladstone's approach in 1870) might make Germany abandon any plans to invade France through Belgium.
Victoria very much loved France, especially Napoleon III who she visited alot when he was exiled to Chistlehurst, so she would most likely be fine with a the formal Entente, more so if it protects Belgium, the homeland of Prince Albert.