In the 2012/13 season, the U-15 team played mainly in attack, scored nine goals in 28 championship matches, and later began to use it more and more in defense. In the 2013/14 season he played in the 1st Slovenian Cadet League, played 25 matches, but did not score a single goal. The following season he played again in the above tournament, played 26 matches and did not score a single goal. In the 2015/16 season, he played for the first time in the Youth First League of Slovenia. As a major defensive player, he played 29 matches and scored one goal. In the 2015/16 season, as in the following season, Rom was on the list of players of his team who played in the UEFA Youth League.
In the 2016/17 season, the young defender continued to play regularly in the youth championship, played 21 matches and scored four goals. He also trained with a professional team, for which he played three matches in the championship that season. He made his professional football debut on December 10, 2016 in a victorious (3: 2) home match against the future champion of "Maribor", head coach Simon Rozhman allowed Matiia to play a full 90 minutes. Starting from the next round and throughout the spring part of the championship, he sat on the bench and returned to the main team only shortly before the end of the season.The club finished the championship in the 2016/17 season in fourth place in the table, which meant that the team secured a place in the first qualifying round of the UEFA Europa League 2017/18. In the 2016/17 Slovenian Cup, "Domžale" reached the final, where they won 1-0 thanks to a goal by Haber Dobrovolc. Matiia Rom did not take part in any game, and the final match was on the bench.
The next season of 2018/19 started for the right defender, as the previous one ended. He missed the 2018/19 Europa League qualification of his team, which was eliminated in the second qualifying round after four consecutive draws, and also played after that occasionally. At the end of November 2018, he played only six matches in the league, but on December 1, 2018 he became the main defender of his home club, when he made a goal assist in a lost (1: 2) match against the dominant "Maribor". After that, the 20-year-old defender was used in all matches of the championship until the end of the season and played a record 25 matches in the top division and scored three assists. With the team once again took third place in the final table and, thus, again secured a place for the team in the European Cups. In the Slovenian Cup 2018/19, Matiia played in two matches, and "Domžale"lost in the quarterfinals to "Maribor".
In the 2019/20 season, Rom increasingly remained on the bench and was rarely used until the winter break. In the 2019/20 Slovenian Cup, in which he played two matches, he and his team were eliminated in the quarterfinals by "Mura". After playing only six matches in the championship this season, in early January 2020 it was announced that he would transfer to the Croatian club of the First Division "Inter" (Zapreshych). He signed a contract with a team from the town of Zaprešić, near the Slovenian border, until June 2021.
On December 1, 2020, he signed a contract with "Kolos". He made his debut in the T-shirt of the Kovalivka club on December 2, 2020 in the victorious (4: 0) away match of the third qualifying round of the Cup of Ukraine against Vinnytsia's "Niva". Matiia went on the field in the starting lineup and played the whole match . He made his debut in the Premier League of Ukraine on December 12, 2020 in a draw (2: 2) away match of the 13th round against "Dynamo" Kyiv. Rom came on the field and played the whole match.
He played 49 matches for the youth national teams of Slovenia in the age categories from U-15 to U-21.