Corner outfield spots are pretty interchangeable in the skill set they require. Left field and right field are so interchangeable that at some point, someone started lumping them together and referring to the group as "corner outfielders".
The only real difficulty in transferring a player from one corner to the other would be an issue of familiarity and comfort. Alex Rios--apparently evicted from center field without it even really needing to be said--is familiar with right field, and would be more comfortable there.
"I like center and right because those are the ones I’ve played. I think I played left last year. It’s different. Center and right is different than left. We’ll see what happens."
Well, that's simple enough to accommodate, and apparently Robin Ventura is just the type of manager to say "Yeah, sure, whatevs."
As Tom Fornelli pointed out, Rios has played 701 games in right field, and since he's already demonstrated a tendency to let struggles in one area of his game bleed out to every other component of his worldly existence, perhaps an effort to make Alex a bit more comfortable is prudent--even if all his crappy play kinda makes you want to do the baseball equivalent of assigning him to an outpost in Siberia.
There is one difference in the physical requirements of left field and right field, and that's the throwing arm.
Throwing ability is without a doubt the least important asset of an outfielder. Speed, instincts, routes, and actually catching the darn thing are way ahead on the priority list, but after all that, you generally want the stronger arm in right field in order to make the long throw to 3rd base.
As a defender, throwing arm also happens the only real tool Dayan Viciedo has. He's still years away from being an albatross out in the field, but results come up from a google search of "Dayan Viciedo lawn ornament". What he does have is a gun, and it would nice to see him utilize it as much as possible. Not necessary, not even really a luxury, just nice.
Rios can throw a bit too, though. In fact, during his prime he routinely graded out as saving several runs above average according to multiple defensive metrics on the strength of his arm alone. Recently, as his career descended into the tar pit, his arm has become more regularly identified for it's sidearm motion, its resemblance to an amateurish attempt to throw a 2-seam fastball, and for nearly gouging Gordon Beckham's eyes out. Still, he's got some power in his right shoulder, and the notion of him returning to be an effective thrower is not absurd, and at least no worse than the notion of him returning to be an effective hitter.
Everyone would probably like Alex Rios more if he were contrite to a fault about his dreadful year, and eager to re-prove himself beyond caring about his particular assignment. Instead Rios is being up front about what he feels comfortable doing, and it's probably going to prove more useful than him trying to ingratiate himself. Especially if it's going to be so darn insignificant.