I haven't read the book. Does it really go so far as to say that the girlfriend should say all that but shouldn't say "I would like it if you would do that"?
'Cause there's a big difference between "I don't tell him what to do" and "I don't express my preferences/desires".
No, it is totally fine to make requests! NVC just advises you to give some context about your feelings and needs before you make the request, instead of jumping straight to it. The prescribed sequence is:
1. Observations: things that are objectively observable
2. Feelings: your feelings about them
3. Needs: the needs you want met
4. Requests: a proposal as to how you want your needs met
It's not always practical or necessary to go through the whole sequence. Sometimes all you need to say is "I'd like you to stay." But if things get tricky or contentious, it can help a lot to separate observations from feelings, and start with objective facts first.
For example, if someone is really upset that their partner isn't staying home with them, they might be tempted to say "Obviously you don't care about this relationship because you never spend time with me!"
That's not going to work nearly as well as "When you leave me at home alone a lot, I feel lonely and ignored. I need time and connection to feel good about our relationship. Could you stay home tonight?"
Explaining your feelings serves (at least) two purposes: (a) it helps the other person have empathy for you; and (b) it provides information about the true purpose of the request. The extra information helps ensure the right need is addressed (in this case, it reveals that what's wanted isn't just presence at home; it's quality time and connection), and helps the other person find alternative solutions if they can't accept the proposal (maybe their partner has an appointment to visit a friend at the hospital and really can't stay; but they are still many ways to address the underlying need, e.g. "It's important that I see my friend at the hospital, but I do want to spend time with you; can we make a plan to spend tomorrow night together?")
If the only information provided is the request, then the receiver can only say yes or no; they aren't equipped with enough information to find a solution that might work better for both parties.
(I guess I should add that this is my interpretation; it seems like people have different interpretations of NVC. I think of it as a tool to use when things get difficult, and for me its purpose is to convey information more clearly, not to obscure my true preferences.)
'Cause there's a big difference between "I don't tell him what to do" and "I don't express my preferences/desires".