It's probably just the date on which the engraving was done -- Vladivostok itself was in a long period of "transition" all through the 1920s, but nothing really major happened in November 1926.
Some of the names are very clearly Japanese, as I confirmed by Googling -- apparently, it was a gift from a group of six people, and thus there are six surnames given: "From Hayasi, Yakusiei, Iwahashi, Nakayama, Arisaka, and Kodo." And "Daito" is also a Japanese surname.
As the wikipedia article on the History of Vladivostok explains, there was a significant Japanese presence in the city for many decades, and from 1917-1922 the city was occupied by a coalition of foreign troops that included Japanese soldiers. After the occupying militaries left in 1922 and the Bolsheviks took control of the city, the number of foreign residents and foreign businesses began to decline, but this didn't happen overnight.
So, I might speculate that the cup commemorates the closing of a Japanese business, presumably a firm owned by "Mr. Daito". In that case, the significance of the cup can be interpreted as "So long, Boss, thanks for the good years -- XOXOXO, Your Staff."
On the other hand, it might have been an occasion of far less gravity than a Bolshevik-forced exodus of foreign capitalist dogs. Maybe Mr. Daito wasn't the owner, but simply an older employee who was retiring. Or maybe these seven people weren't coworkers at a firm, but a group of friends, and "17 November" was Daito's birthday!
But we can't be sure what the actual occasion is, because на добрую память isn't at all specific -- it's literally "to nice recollections," and when engraved on a souvenir or written in a gift card, it conveys "[We hope that looking at this gift in the future will bring you] pleasant memories." But memories of WHAT, the cup doesn't say.