How do you drink ginger? Ginger is a root. I think it's more appropriate to say "I like drinking hot ginger tea."
It’s kinda similar like hot chocolate or a cup of coffee. The fruits have the similar name, it doesn’t mean that we have to add ‘tea’ or ‘drinks’ just because it’s diluted with water. Especially in context of jahe as drinks in Indonesia, jahe panas and the jahe have different level of concentration.
The Indonesian sentence is fine. But in English we can't say "drink hot ginger;" and omit the "tea," because we do think of ginger as a solid.
This is less of a vocabulary issue than a cultural one - jahe panas is perfectly understandable in Indonesia but hot ginger is not for English speakers. Typically it's called hot ginger tea, even if no actual tea leaves are used.
When I was in Indonesia and saw Ginger on the beverage section, they will always add teh on the end or put it in the teh section.