Is ghusl required if a white liquid—other than semen—is discharged from the penis after arousal?

What the questioner finds is madhy (pre-seminal fluid). Its ruling is that it only necessitates washing the penis and whatever part of the garment and body it touched, and performing ablution (wudu'). The Prophet, peace and blessings be upon him, said to Ali: "If you see madhy, perform ablution and wash your penis."