Must one interrupt the prayer or renew the ablution due to the continuous and involuntary emission of gases from the anus during prayer, knowing that this does not fall under the category of fecal incontinence?

If the discharge is continuous such that you do not find enough time to pray with a valid purification, then your ruling is that of one afflicted with perpetual discharge ( سلس); perform ablution for each prayer after its time has begun, and pray as much as you wish until the time for that prayer expires. If the discharge is merely dry gases, then nothing else is required of you. However, if it is feces or similar, then use a piece of cloth (to contain it). If you find sufficient time to pray with a valid purification, then wait, perform ablution, and pray within that time. Istinja’ (washing the private parts) is not obligatory for mere wind, but only for what soils the area. If what you are experiencing is whisperings (وسوسة), then disregard them.