On 2 July 2014, Domgjoni signed his first professional contract with Kategoria Superiore side Tirana after agreeing to a five-year deal.
[10] Seventeen days later, he made his debut in a 1–0 home win against Partizani Tirana after coming on as a substitute at last minutes in place of Regi Lushkja.
[15] His debut with Luzern came four days later in the 2021–22 UEFA Europa Conference League third qualifying round against Dutch side Feyenoord after coming on as a substitute at 63rd minute in place of Patrick Farkas.
[18] His debut with Termalica came two days later in a 2–1 home win against Jagiellonia Białystok after coming on as a substitute at 73rd minute in place of Kacper Śpiewak.
[23] Three days later, Domgjoni made his debut with Albania U17 in a 2014 UEFA European Under-17 Championship elite round match against Italy U17 after being named in the starting line-up.
[25] Four days later, he made his debut with Albania U19 in a match against Malta U19 after being named in the starting line-up and scored own goal during a 0–1 home defeat.