It depends if the punishment has been legally or extra-legal decided and would be extra-legally carried out. Such claims are always a matter of opinion and whose law, but not all opinions are equal.
1. Threats Made by the US Government:
Obama's statements such that Snowden is not worth the effort of an expensive extra-legal killing (“not going to be scrambling jets to get a 29-year-old hacker”) by a president that has engaged in many extra-legal killings, at least one against a US citizen, is a threat of extra-legal action. For instance if someone sent a letter that said "I'd kill you but you aren't worth the bullets" would be interpreted by many courts as a threat. Furthermore direct threats of extra-legal killing have been made by other members of the US government.
2. Prior Actions Against Snowden:
The fact that Obama has attempted to use trade deals and threats to prevent Snowdens asylum appeals suggests that Obama and the US government is not willing to give Snowden a fair hearing since they are manipulating the international system of asylum to prevent him from getting a fair hearing internationally.
3.Prior Pattern of Action Against Other Whistle Blowers:
Obamas illegal treatment of Bradley Manning is part of a pattern going back before Obama of illegal mistreatment of whistle blowers by the US government.
Given this evidence I would argue that the threat of extra-legal punishment is very much real and has been publicly communicated to all involved parties. The reality and communication of this threat to Snowden makes a very strong case for the claim that he has been extra-legally exiled.