I know you use verb stem+始める when you want to indicate that something started, so would this sentence be correct?
特にゲームをする始めます。
I know you use verb stem+始める when you want to indicate that something started, so would this sentence be correct?
特にゲームをする始めます。
The conjugation before verb is 連用形(masu-form), so your sentence is incorrect. ゲームをし始めます is correct. For example, "start walking" is 歩き始める. 歩き is 連用形 of a verb 歩く.
In addition, 特に is unnatural in this sentence.