In 2016, Kenzhebayev traveled to Milan, Italy, for an under-14 tournament as part of the academy of Dordoi Bishkek of the Kyrgyz Premier League.
[4] In July 2023, it was reported that Kenzhebayev was leaving FC Dordoi Bishkek to join Slavia Mozyr of the Belarusian Premier League on a three-year contract.
He had made four total appearances in the Kyrgyz Premier League for Dordoi Bishkek during his tenure with the club.
[7] In January 2025, it was announced that Kenzhebayev was loaned to newly-formed Kyrgyz Premier League club Bars Issyk-kul for the 2025 season.
He tallied a goal and an assist in a 6–0 victory over Brunei to close out qualifying and advance to the final tournament.