Is “European Peninsula” a common name for Europe?

'Europe' as a continent, includes part of Russia, so I imagine the journalist was trying to avoid contradiction by using a phrase that, though uncommon, is clear. Nothing more complicated than that.

A peninsula is any land that is surrounded on three sides by water, just as an island is land completely surrounded by water. Debate as to whether Europe could be considered a peninsula is comparable to debate over whether Australia (or indeed any continent) could properly be considered an island. That is, by a pedantic reading of the definition, yes, Europe is a big peninsula jutting out of the west of Eurasia. But no, no one ordinarily refers to it as such or treats it as such.

One might refer to the American experiment or the the lucky country for poetic effect, but unlike these expressions, European peninsula is not a set phrase. Europe is traditionally considered a continent in its own right, indeed, the Continent. But the author would not have chosen this phrasing idly. The article is published by a US-based international affairs research firm, and I believe the phrasing is intended to draw attention to Europe's vulnerability with respect to an aggressive Russia— as if the whole landmass of Europe were no different from Crimea.

According to National Geographic, who really ought to know about these things, Europe can indeed be considered a peninsula sensu stricto:

Europe is the second-smallest continent. Only Oceania has less landmass. Europe extends from the island nation of Iceland in the west to the Ural Mountains of Russia in the east. Europes northernmost point is the Svalbard archipelago of Norway, and it reaches as far south as the islands of Greece and Malta.

Europe is sometimes described as a peninsula of peninsulas. A peninsula is a piece of land surrounded by water on three sides. Europe is a peninsula of the Eurasian supercontinent and is bordered by the Arctic Ocean to the north, the Atlantic Ocean to the west, and the Mediterranean, Black, and Caspian Seas to the south.

Europe’s main peninsulas are the Iberian, Italian, and Balkan, located in southern Europe, and the Scandinavian and Jutland, located in northern Europe. The link between these peninsulas has made Europe a dominant economic, social, and cultural force throughout recorded history.

All bold emphasis above is my own.

Now before anybody gets all het up and bent out of shape, National Geographic in its encyclopedia entry on continent explains that there are nonphysical considerations to what is or isn’t historically considered a continent:

Coastlines, however, do not indicate the actual boundaries of the continents. Continents are defined by their continental shelves. A continental shelf is a gently sloping area that extends outward from the beach far into the ocean. A continental shelf is part of the ocean, but also part of the continent. If continental shelves were included in the total land area, continents would make up more than one-third of the Earth’s surface.

“Continent” has more than just a physical definition. To human geographers, the term is about culture. The continents of Europe and Asia, for example, are actually part of a single, enormous piece of land called Eurasia. But linguistically and ethnically, the areas of Asia and Europe are distinct. The various cultural groups of Europe have more in common with one another than they do with cultural groups in Asia. Because of this, most geographers divide Eurasia into Europe and Asia. An imaginary line, running from the northern Ural Mountains in Russia south to the Caspian and Black Seas, separates Europe, to the west, from Asia, to the east.

So we all pretend this imaginary line separates one continent from another. It’s a “culturally-correct” myth in that disabusing someone of their cherished myth is tantamount to goring their sacred cow. People will find it insulting to their culture to call them out on it.