IMHO this is terrible advice. I don't believe that ultimatums have any place in marriage, ever. All he will achieve is adding to the resentment she's already expressing, and make things worse.
Sex meets many of my needs for emotional and physical intimacy. The best that any of us can do is express our needs to our spouse and let them know how deeply the issue is affecting us and the marriage. Often times the problem is that communication has broken down and the hurting spouse doesn't know how to express their needs or their hurt. The other spouse may not realize that sex is about more than enjoying physical pleasure. That is one of the functions of marriage counseling ; to help spouses communicate their needs to each other, and to seek balance. There have been many posts here and on other message boards from spouses who say that they had no idea that sex meant so much to their partner beyond physical pleasure.
Ultimatums are usually a desperate attempt to communicat the depth and severity of a problem, but they are not communication. Once the nature of the hurt has been sucessfully communicated and understood through other means, then there is a reasonable expectation that an effort be made to solve the problem. If the fact that I am lonely and hurting isn't enough to motivate my wife to re-establish intimacy, then a demand isn't going to do it either. If there are no health or physiological reasons for any issues in a marriage, and a spouse doesn't want to address the problems, then clearly the fundamentals of the marriage have broken down. At that point we can encourage change, but we can not demand it.
To the OP my suggestion is to make every effort to communicate exactly what you get from sex. If you don't understand what you get emotionally from sex, then take some time to learn and understand the role that sex plays in a marriage. Then communicate your needs in terms that address your emotional, and even spiritual connection to her ; that you want and need to feel close to her, that sex is a deep and intimate connection, and so forth. Put it in terms that clearly show that this is about her, your love for her, and your marriage to her.
Once you've expressed your needs, no ultimatum is going to make her want to meet them. She either wants to or doesn't. If she shows no interest in creating a better and more intimate marriage, then you have a choice. The best anyone can do is either decide that other parts of the marriage are worth choosing to live with it, or get a divorce and move on.
I wish you the best