Here is the text of Edward Snowden's statement about asylum. The key part for Latin America:
I announce today my formal acceptance of all offers of support or asylum I have been extended and all others that may be offered in the future. With, for example, the grant of asylum provided by Venezuela’s President Maduro, my asylee status is now formal, and no state has a basis by which to limit or interfere with my right to enjoy that asylum. As we have seen, however, some governments in Western European and North American states have demonstrated a willingness to act outside the law, and this behavior persists today. This unlawful threat makes it impossible for me to travel to Latin America and enjoy the asylum granted there in accordance with our shared rights.
I am not sure why Venezuela's offer is "now formal" while the others are not, since he asked and they said yes.
Regardless, he has quite a problem because he can't leave, yet I cannot see Vladimir Putin allowing him to stay there indefinitely, a la Julian Assange in the Ecuadorian embassy. I've been saying over and over that Snowden himself is a lot less important to governments than people seem to claim. Putin will do what he can to use Snowden for his own benefit, and Russia is not a particularly safe place for him.
Venezuela is not safe either, especially since a change of government is a very real possibility. Venezuelans may themselves wonder how they benefit from his presence.
Neither option is good. His freedom is in the hands of Nicolás Maduro and Vladimir Putin. One is incompetent and one is plain dangerous.