this is Putin's opinion (question is whether it's legally correct) - original russian and my translation:
"Он приехал как транзитный пассажир — и ему не нужна ни виза, ни другие документы. Он как транзитный пассажир имеет право купить билет и лететь, куда он хочет, — подчеркнул российский лидер. — Он не пересекает государственной границы, поэтому ему виза не нужна", — рассказал Путин. (src: Interfax)
He came in as a transfer passenger - he does NOT need either a visa or any other documents. As a transfer passenger, he has a right to buy a ticket and fly wherever he wants. However, since he did not cross the border of the State of Russia, he does not need a visa.
Bolded text the most critical. Note the fancy quibble - he did not cross the border... yet, it does not say that he's not inside the borders.
... "Что касается возможной выдачи куда бы то ни было, то мы можем выдавать каких-то граждан иностранных государств только в государства, с которыми у нас есть соответствующие международные соглашения о выдаче преступников", — сказал российский лидер, добавив, что с США такого соглашения Россия не заключала.
"Regarding possible extradition to anywhere, we can only extradite people to states which we have corresponding international extradition agreements with", adding that Russian did NOT have such an agreement with USA.
So, to address the actual question:
Putin's statement implies that they CAN arrest and extradite Snowden if they wanted to. He merely says the won't do so in this specific case due to lack of extradition agreement, NOT ebcause they lack jurisdiction.
Other sources disagree. For example:
"A person may stay in a transit zone indefinitely. A state has no jurisdiction over that area," Eugeny Varshavsky, a former head of the Russian Federal Migration Service (FMS) Department for Legal Support, told Xinhua in an exclusive interview Tuesday.
"Anyone in a transit zone enjoys immunity like a foreign diplomat: He or she cannot be arrested, interrogated or otherwise be restricted in freedom," Varshavsky said.
"If the state believes a person violates this country's law or poses a security threat, deportation may be considered, but only to the country of his or her citizenship," he added.
The minister's remarks were correct because, technically, a transit zone's legal status was somewhat similar to the status of the open sea, Varshavsky said.
Such an area had a special legal regime governed by Geneva and the Hague conventions, as well as international transit regulations, he added.
Another wrinkle: Russia's rules seem to require holding a "transit visa" to STAY in transit zone. From http://www.russianembassy.org/page/transit-visa
Transit visa is required if the period of stay in Russia exceeds 24 hours or a traveler needs to change the airport.
But he may possibly have one