Other countries can look at that passport and make their own decision - for example, I've anecdotally heard from people that having a passport stamp for Israel can make border crossings into certain middle eastern countries much more complicated.
Now, the US in effect is saying, "We believe this person to be a bad guy, and you should not trust him". Since he has been charged with a number of crimes, this is a fair statement.
This is the same thing that happens with people in the US who are considered a flight risk from prosecution - their passport is flagged and they are required to turn it in.
One of the many reasons why Snowden's behavior in first revealing himself then leaving hong kong to Russia is very odd is exactly this - how could he not know they could revoke his passport? What did he think would happen?
Countries don't provide (or revoke) your right to travel outside of their sovereign jurisdiction (which would be contrary to the entire idea of sovereign jurisdiction); they can, however, revoke their willingness to represent to other countries that they have some kind of relationship with you. (They can also stop you from exiting their jurisdiction while you are still inside it, and though the US would have liked to have done that in Snowden's case, it didn't have the opportunity.)
Its the country you are currently in and the one you are attempting to enter that control whether or not you have the "right" to travel.
I understand stopping someone from leaving the borders due to legal reasons. But being able to stop your travel once you're outside the country? No.
Revoking a passport isn't revoking citizenship (governments, right or wrong, can do both, but they are separate and distinct acts.)
> But being able to stop your travel once you're outside the country?
Revoking your passport is basically your country no longer vouching for you. Other countries choose whether or not this should impact your ability to travel.
