Golyshev played as a youth within hometown club,
Molot Perm, before joining
Avtomobilist Yekaterinburg as a junior in the
2012–13 season. Golyshev made his professional debut in the
Kontinental Hockey League with Yekaterinburg during the following
2013-14 season. Having been the longest tenured player in completing his eighth season with Avtomobilist Yekaterinburg in the
2020–21 season, placing fifth in team scoring with 27 points through 53 games, Golyshev left the club following a first-round exit to
Avangard Omsk. With the New York Islanders still in possession of his NHL rights, Golyshev was signed to a one-year, two-way contract to immediately join the division-leading club during the pandemic-delayed
2020–21 season on 20 March 2021. He remained on the roster throughout the Islander playoffs push to the semi-finals, without featuring in a game. As a restricted free agent, Golyshev agreed to terms on a one-year, $750,000 contract with the Islanders on 23 September 2021. After attending the Islanders 2021 training camp, Golyshev having left a positive impression, was assigned to begin the season with
American Hockey League affiliate, the
Bridgeport Islanders. Golyshev posted 5 goals through 15 games with Bridgeport before he was recalled to the Islanders through the club's crisis with
COVID-19 amongst the roster. Returned to the AHL without featuring with New York, Golyshev, seeing limited opportunity, opted to be placed on unconditional waivers to mutually terminate his contract with the Islanders on 8 December 2021. On 14 December, Golyshev signed a contract until the end of the 2021–22 season with Avtomobilist Yekaterinburg. ==Career statistics==