A White Russian victory butterflies the near-entirety of the 20th Century. It's not possible to say what could have become.
We can only speculate as to the nature of the resultant Russian regime, given the general chaos and intrigue rife among the Whites' ranks even as they did battle with the Bolsheviks. A monarchist restoration is not imminent - despite a preponderance of disgruntled aristocrats within the leadership, all of whom looked destined to drop their radical leftist sponsors the minute they saw power beyond the most inhospitable reaches of Russia, the Romanovs are an afterthought by this point, an archaic embarrassment clinging to their absolutist pretensions even as their former Empire burns around them. Nevertheless, I could see them hosted lavishly in Petrograd; after a generation or two, some astute members of the family might even be conceded a little political leverage behind the scenes, such as the French Republic permitted its own royalty in the late-19th Century.
Also off the cards, unfortunately, is a situation remotely resembling that of the Weimar Republic in its best days. This has little to do with any public disinclination at the time towards liberal or social democratic elements - as illustrated by 1917's Constituent Assembly elections, the opposite was true. Russian democracy, in the aftermath of a White victory, simply isn't going to be given breathing space. After a brief, awkward, mostly fallacious flirtation with popular government, dominated by a host of closet reactionaries ready to lend occasional lip-service to the big issues, the Russian Republic is going to come out looking a strange blend of paternalistic dictatorship and coalition government, with a dysfunctional coterie of blue-bloods, nationalists, militarists and classical liberals, concentrated around a commanding personality (Admiral Kolchak springs to mind), holding down power at the expense of virtually everybody else.
The Russian state is going to be a culturally, politically and economically retarded entity. Say what you will about the genocidal excesses of the Soviet leadership, they DID elevate Europe's most backward established power to a position of prestige and tremendous geopolitical influence. Though the Whites may have counted many acute, deviously pragmatic men as leaders, they lacked both drive and ambition, united by no grand ideological vision but a desire to to see the social status quo preserved and proliferated. I've noticed many on here seem to draw an equivalence between the ethic of the Whites and the fascist movements of Mussolini and Hitler, but even that's probably giving them credit - a White state would be more along the lines of a tinpot South American dictatorship than the ostentatious affairs of fascist Italy and Nazi Germany, with little internal consistency and absolutely no direction. The society it presides over will be an essentially agricultural one - attempts to industrialize Russia pre-1914 had resulted in a situation where peasants flocked to the cities as a means of making an extra buck when they weren't attending the fields, not the establishment of a stable working class, and I see no reason why the Whites would object to enduring down this path. Whether it will be much generally poorer than the Russia we know is debatable, but it definitely won't be wealthier, and much of the landmass (Siberia, in particular) will remain underdeveloped and unsettled, even by contrast with today's circumstances.
On the international stage, things become hazy. It's dangerous to consider the presence of a 'Red Menace' in Eurasia the primary driving force behind the rise of reactionary rightism in the early-20th Century, but, with Russia emasculated and insular-looking, no-frills conservatives of the Hindenburgian variety are likely to dominate politics in Italy, Germany and elsewhere - without the prominence of Marxism, there will be no need for a conscious rightist effort to synthesize socialist ideas with their own values. These will likely be dry movements, at the very least a touch more rational than the demagogic projects we saw IOTL, whom may, ironically, look to White Russia as an enviable model of government and society. In Germany, there may be establishment yearnings for the acquisition of new territories in the East, or even the reclamation of lost colonies overseas; at any rate, expansionism will manifest as an exercise in realpolitik, not the harebrained initiative of a death cult driven by quasi-religious ideological fervor. Taking the USSR out of the picture also eliminates much of the urgency that accelerated drives towards welfare reformism in Western Europe; Britain and France are going to be a lot more quintessentially conservative societies, closer to the United States in terms of their institutions and attitudes. IOW, the Western political landscape of the 20th Century will come to resemble that of the 19th Century, with power politics and unabashed imperialism trumping intellectualism and ideological snobbery.