Euwe had an older brother, Willem and younger siblings, Annie, Kees, Tiny and Bob. His father was a primary school teacher who gave violin and piano lessons on the side. His mother, Elizabeth, whom he remembered as a rather sickly woman (who wouldn't be after six kids?) was a fanatical chessplayer. His parents played each other regularly on their "chess night." Although she was a chess fanatic, she was never really very good; when Euwe won the world championship in 1935, the next year she entered the Dutch Ladies Championship but did not do well. Research did not turn up any games from that tournament which was won by Catharina Roodzant (October 21, 1896 - February 14, 1999); she won the championship three times, 1935, 1936 and 1938.
His older brother, Willem (known as "Wim"), was born December 22, 1899 and was employed as an engineer in the patent office. A search of Dutch genealogy sites indicated that the date of his death is unknown. According to a post on Chessgames.com there's a thesis by him published in 1928 titled Differential invariants and partial differential equations in tensor calculus, suggesting that he was a mathematician like his brother. There's also a few meteorological studies which he published while working for the meteorological and geophysical service in the Dutch Indies (now Indonesia).
The following game is the only game by the "other" Euwes that I was able to locate. The game was played in an Eindhoven (a city in southern Holland) telex match in 1937.
Following a series of experiments on various wavelengths in 1925, reports of good reception from a low-power shortwave transmitter were received from Jakarta on March 11, 1927. Dutch Queen Wilhelmina made what is believed to be the world's first royal broadcast on June 1, 1927, addressing compatriots in the East and West-Indies. Shortly afterward regular international broadcasts in Dutch were made from the Philips Radio shortwave transmitter in Eindhoven to the Dutch Indies.
One of the first air raids in World War II was flown by the RAF on December 6, 1942 targeting the Philips factory in Eindhoven and 148 civilians died even though the attack was carried out on a Sunday. Large-scale air raids, including the preliminary bombing during Operation Market Garden to aid the US 101st Airborne Division paratroopers in securing the bridges in and around the town on September 18, 1944, destroyed large parts of the city. The reconstruction that followed left very little historical remains. From this information I assume that Euwe's opponent may have been a player from the Dutch Indies.
In the game Euwe conducts a strong attack against his opponent's King.