Situation: There is this guy at my job who business dev and is acting like"Co-CEO" although he doesn't have the official title or authority, just because he is good at selling ideas and CEO is a beta while he is alpha. He is trying to put his nose into every department of the company. He hasn't accomplished anything in 2 years and keep changing priorities and hiring people (wasting money) while just keeping the CEO thinking he is actually managing stuff. My boss who is also a beta doesn't back me up with certain decisions and even though he agrees with me in certain aspects that this guy is wrong but magically changes his mind after speaking with this guy.

I have been working on a project which that business dev guy was not involved for the last 6 months and can be a huge win for the company. I'm in the last stage of implementation and this guy started out of the blue putting his nose in my project by shooting necessary requirements and tried to assert dominance (he asked me to change things and I said I didn't agree and he got pissed). The next 2 days he put pressure on my manager and scheduled a meeting to force me to accept his dominance (he doesn't even care that much about the project success, but whether or not I'm obeying him, I think he is a narcissist). I agreed with my boss to hire the right person to do the final part which is key to launch the project and the CEO has been waiting for years for this project to be started/done.

My boss actually started the project but could not get anything done and got in conflict with other people in different departments, while I tried to solve the problem by looking into different people's needs. This alpha guy said I should not choose my outsource but work with a girl who is on a maternity leave and doing part-time work - she a recent grad and doesn't know shit., but she obeys him and her husband is working for this business dev guy also "trying ideas" for 6 months with no success.

This guy usually forgets what he asks for and I managed to not do what he asked because he forgot or changed his mind with a new idea (he is pathological ADHD), but never forgets when I say no to him.

So I'm wondering, should I just keep ignoring and doing my thing and focus on the success of the project so I can boost my reputation with the CEO or should I just confront him to build respect?

It's one of the biggest opportunities in my career and I will not let him screw up this project. One person I talked with said you should never confront a narcissist but I'm still not sure whether or not he is one.

Note: he can't get me fired for subordination, first because he is not officially my boss although he is trying at all costs forcing under him and manipulating my boss. Both of them have "equal" status in the official hierarchy of the company but my boss always gives away power to him for reasons I don't understand.