An undrafted free agent from Morden, Manitoba, Genoway graduated from the University of North Dakota as the fourth-highest-scoring defenceman in UND history with 127 points in 168 career games. His 168 games are tied for the most by a UND defenceman, and he also ranks tied for second all-time among UND players rearguards in game-winning goals, fourth in power-play goals, fifth in assists, and seventh in goals. Upon completion of his collegiate career, Genoway was signed to a one-year entry level contract with the Minnesota Wild on April 12, 2011. In the 2011–12 season, his first as a professional, Genoway was assigned to AHL affiliate the Houston Aeros. In 72 games as a fixture on the Aeros blueline, he scored 7 goals and 36 points. He received his first NHL recall at the tail end of the season and made his NHL debut, registering an assist, in a solitary game for the Wild against the Phoenix Coyotes on April 7, 2012. On June 29, 2012, he was re-signed to a one-year extension with the Wild. After 52 games with the Aeros during his second season within the Wild organization in 2012–13, he was traded to the Washington Capitals in exchange for a conditional seventh-round pick on March 14, 2013. On August 1, 2014, having left the Capitals organization as a free agent, Genoway signed abroad on a one-year deal with Dinamo Riga of the Kontinental Hockey League. After a year in Riga, he moved on to fellow KHL team HC Spartak Moscow, where he spent the 2015–16 season. In May 2016, he signed with Jokerit, a Helsinki-based KHL team. In the 2018–19 season, Genoway played under a one-year contract with Frölunda HC of the Swedish Hockey League. Genoway contributed to a highly successful season with Frölunda recording 9 goals and 25 points in 51 games in claiming the domestic Le Mat Trophy. He also led defenseman in points throughout the tournament to help claim the 2019 Champions Hockey League. At the conclusion of his contract with Frölunda, Genoway opted to return to the KHL, agreeing to a one-year contract with Russian club, Torpedo Nizhny Novgorod on May 7, 2019. Genoway established new career highs in the KHL during the 2019–20 season, notching 25 assists and 31 points in 62 regular season games. As a free agent, Genoway opted to continue in the KHL, securing a one-year contract with Avtomobilist Yekaterinburg on May 4, 2020.
