Artiom began his career at Zimbru Chisinau in the 2005–06 season. Zimbru finished in second place in the Moldovan National Division in his first season in senior football, with Gaiduchevici playing in two of their twenty-eight league games.[3] This lack of first-team action prompted the goalkeeper to move to FC Iskra-Stal, who had just been promoted from the Moldovan "A" Division. Gaiduchevici hoped that he would stand a better chance of becoming the club's first-choice goalkeeper than at Zimbru.
FC Iskra-Stal finished in ninth place in the Moldovan National Division in 2006–07 season, but Gaiduchevici played a peripheral role. He made more of an impact in his second season at Iskra-Stal, 2007–08, making twelve appearances as the club finished in an improved sixth place. In 2008–09 both Gaiduchevici and Iskra-Stal improved again, with the goalkeeper playing in twenty-three of their thirty league games and cementing his place at the club's first choice goalkeeper. Iskra-Stal claimed third place in the Moldovan National Division, qualifying for the 2009-10 UEFA Europa League. Gaiduchevici made his debut in Europe in the 3-0 home loss to PFC Cherno More Varna of Bulgaria on 23 July 2009.[4] He also played in the 1-0 away loss to Cherno More that saw Iskra-Stal crash out of the UEFA Europa League on aggregate.
The following season, Iskra-Stal again qualified for the UEFA Europa League by finishing as 2009-10 Moldovan National Division runners-up. Artiom played in all but one of the club's thirty-three league matches. 2010–11 turned out to be Gaiduchevici's last for Iskra-Stal. After making twenty league appearances in the first half of the season, he left before the season's finish to join the league's eventual winners, FC Dacia Chişinău, signing a two-year contract with his new team. At the end of his spell at FC Iskra-Stal, Artiom had a record of just 55 goals conceded in 76 matches, a record that had attracted big teams such as Dacia.[5]
Making his debut in a 2-0 win over FC Tiraspol on 26 February 2011,[6] Gaiduchevici made a total of seven appearances in 2010–11 for Dacia as they won the Moldovan National Division.[7] This championship win qualified the club for the 2011-12 UEFA Champions League, where they were drawn against FC Zestaponi of Georgia in the second qualifying round. Gaiduchevici played in both the away leg on 13 July 2011, where Dacia were beaten 3-0 in Zestaponi, and the home leg on 20 July where even a 2-0 victory was not enough for Dacia to progress to the next round as they were defeated on aggregate.