Without context, I suppose it's ambiguous. At first, I understood it as "please let me off here/please drop me off here". I guess technically it can also be interpreted as the book suggests. We have
- (transitive with object following “get”, slang) To excite or arouse, especially in a sexual manner.
Catwoman's costume really gets me off.
- (intransitive, slang) To experience an orgasm or other sexual pleasure; to become sexually aroused.
You are not allowed to get off in my bedroom.
It takes more than a picture in a girlie magazine for me to get off.
I'm assuming that what the book is trying to say is that please let me off here is correct as a request to exit a vehicle, like a taxi, whereas please get me off here is incorrect and that it has a sexual meaning to it. I agree that it is incorrect in the case. It doesn't make sense as a request to exit the taxi. But I'm not confident that it would be understood in a sexual manner. It doesn't really seem idiomatic when talking about getting excited, at least in AmE. In other words, I don't think please get me off here will be understood in an "excited" sense by most people, unless the surrounding context somehow supports this usage. Then it would likely mean getting one of the persons to orgasm.
Generally though, get off is used like in the example given in the entry above, X gets me off, where X is the thing from which excitement is derived. There is also the related get off on:
get off on sth
-phrasal verb with get
to find something exciting, especially in a sexual way:
Dave likes power - he gets off on it.
Please get me off here, or please get me off of here, can be used to mean please remove me from here in a situation where you are ordering someone else to remove you, for example, while you're stuck on a broken roller coaster ride.
Oh my god, the ride's stuck! Please get me off here now!