I would say the world is going more lefty, with governments consolidating their power bases and censoring/silencing criticism.
The world is going neither "right" nor "left", it's going more authoritarian on an orthogonal axis.
It's the left that wants to grow the size of government and have it spy on/manipulate as much of peoples' lives as it can. It does this under the guise of benevolence, of 'caring' about the plight of some group, real or imagined, varying by context. The right wants smaller government and more liberty for the individual.
No, the authoritarian left (e.g. US Democratic Party) wants to manipulate people through government. The authoritarian right (e.g. US Republican Party) wants to manipulate people through privatized industry. Neither is interested in leaving people alone.
There are those, on both the left and right, who actually do want smaller government and more liberty for the individual, but they are not in power in either major US political party.
If you are the sort who stalwartly votes party lines, I would strongly suggest you reevaluate your loyalties, democrat or republican. At this point, this is the only way to fight the orwellian lunatics in power now.
Indeed; the only hope is to vote independent, libertarian or green.