Skundrich grew up in Pennsylvania, where he attended Hempfield High School.[2] He played four years of college soccer at Stanford University between 2014 and 2017, where he made 82 appearances, scoring 9 goals and tallying 13 assists. He was captain his junior and senior year. During his senior season, Skundrich earned First Team All-Pac-12 honors as the team won its third-straight Pac-12 Championship. He was also a member of the league's second-team honors in 2016, while collecting conference All-Academic second team honors in 2015.[3]
On February 8, 2021, Skundrich moved to Loudoun United for the 2021 season.[8] On May 12, 2021, Skundrich moved to Loudoun's MLS parent club D.C. United.[9] The next day he made his MLS debut in a 1–0 win against the Chicago Fire.[10] Following the 2022 season, his contract option was declined by D.C. United.[11]
On December 5, 2022, it was announced Skundrich would join USL Championship side Colorado Springs Switchbacks for their 2023 season.[12]