I’m not sure of the answer, but I feel like other commenters are just guessing.
My reason for doubting the dongle is that Bluetooth is designed to be ultra-low-power. We’re talking in the low milliwatts range.
I don’t know how much power a 2.4gHz dongle uses, but I would be surprised if it was less than Bluetooth. However, in terms of laptop battery life, it’s probably not significant enough to really matter. It’s not like either one will cut your batteey life down a noticeable amount.
I don’t think it needs a remaster considering how good the game still looks, but it’s 7 years old now. That’s not exactly “new” anymore.