That's her cousin Prince Michael of Greece.
At first I also thought it was cousin Michael, but I wasnīt sure. I have read Irene and he are close but I didnīt expect them to behave together like this. Michael is no first cousin of Irene, Sofia and Constantine. Michael is a first cousin of their father King Paul I of Greece. Michael's father, prince Christopher, was a younger brother of King Constantine I of Greece, who was in turn the grandfather of Irene, Sofia and Constantine.
Michael and Irene together at an exhibition.
BTW Michael is the father in law of Prince Aimone of Savoy-Aosta, Duke of Apulia, who is married to princess Olga (Michael youngest daughter). Aimone's grandmother was a first cousin of Michael. Michael is married to the Greek artist Marina Karella. This was a morganatic marriage, which resulted in Prince Michael renouncing any rights to the throne of Greece on behalf of himself and his future descendants; this renunciation occurred prior to the marriage, after which the marriage was approved by King Constantine II. Michael and Marina became the parents of two daughters:
Princess Alexandra of Greece (born 15 October 1968), married to Nicolas Mirzayantz, by whom she has two sons, Tigran and Darius Mirzayantz.
Princess Olga of Greece (born 17 November 1971), married to her second cousin Prince Aimone, Duke of Apulia, paternal grandson of Princess Irene of Greece and Denmark, second daughter of King Constantine I. Aimone and Olga are the parents of two sons, Prince Umberto of Savoy Prince of Piedmont (b. 7 March 2009), Prince Amedeo Duke of the Abruzzi (b. 2011), and a daughter, Princess Isabella Vita Marina (b. 2012)
Michael is a paternal first cousin of Prince Philip, Duke of Edinburgh.