May think Cain wants a producer that does what he says, but producers need to be a little tough, they work with all kinds of people. Often have to be the one who puts their foot down and say something has to be done or something won't be going into the game. The game director does this a lot, but the producer will often be the one telling them they are out of time/money or someone they want isn't available anymore.
First key trait may seem obvious but it's good communication. Need to have good communication skills even with people who do not have good communication skills. Many introverted people in game development, and you will have to handle all the different flavors of introversion. You will have people who never want you to come in and talk to them, email them. They'll want you to Slack them instead, or Slack them to get a time to come and talk to them. They may only want you to talk to them during certain hours of the day, or if they don't have a little thing hanging on their monitor (Don't talk to them if they have the thing on, even if they have forgotten to take the thing off, so you don't talk to them all day.) You just have to figure out how to work with them. Cain doesn't think this is entirely people getting full of themselves, he himself has issues with his mental structure of a program falling apart when he gets interrupted during coding. You can generally interrupt Cain whenever he is designing, would rather not when he is programming. But you have to work out a system, you can't just tell the producer never talk to me. Won't just be communicating with developers, but with publishers, press, and management in the company.
Second one is being organized, more than anyone else on the team, you have to be very organized. Game development has many moving parts, lots of half finished things being put in the game. Stuff that isn't completed in the game gets put in because it's what they have, or because they want to test it. Have to keep track of all that. Have to track all of the partially completed assets that are in pipelines. Now that almost everything is worked on by multiple people, you have to keep track of the self-set deadlines to ensure each component is sent off to the next person in the pipeline to be used. Can't expect everyone in that system to know those deadlines, you'll be telling people they need to get something done by Friday when the official deadline is next month. There's a lot of people who are going to need that asset, and you know that.
Third thing is knowing game development works. Some producers disagree with this, Cain has heard from some of them stuff like they might as well be making shoes, he disagrees with that. For example, making modern 3D assets is complicated. First it's modeled, then it is textured, then it is rigged, then it is animated. At every stage, a lot of design needs to be known. The modeler needs to know what it's supposed be shaped like and how big it is, the texture artist needs to know what it looks like and what environments it is expected to be in (Can it blend in?) The rigger has to know what parts to rig, is it ok if it's face isn't that expressive or do you need it to be ready to make a lot of expressions. The animator has to know what animations are needed, maybe it's never going to be attacked and doesn't need a death animation, maybe it needs multiple different death animations for all the different ways it can be attacked. As a bonus, can any of those things be done at the same time? Once model is done, can one person texture it while another person rigs it? Producer has to know that, if they look at the schedule and they see a model is being textured and rigged at the same time, they need to bring it up if they think that can't be done. Maybe your lead artist should have caught that, but making and managing the schedule is the producer's duty at the end of the day.
Fourth thing is proactivity, very important for a producer. You need to deal with problems before they happen, look for chokepoints in the schedule, notice when something has been to assigned to someone on leave/vacation, notice when someone quits and you had something you had scheduled them to do next month. You don't wait to get to the point where that person is needed and now you have a problem, you constantly check the schedule for possible problems and deal with them. Don't replace someone who quit just as you realize you need them for an asset, do that far earlier.
Finally, producers have to be very good at deadlines, figuring them out and enforcing them. They'll be looking at deadlines publishers set (Money, when they expect a demo), deadlines set by press (They want to see a walkthrough at this time showing off features), and localization. Localization needs dialogue locked way ahead of time.
If you think you'll be good at those five, you could be a good producer. To figure that out, go to a company and be an assistant producer. Sometimes they are hired, sometimes they come from other disciplines (Why good communication and good game development knowledge are important.) Cain had some great producers coming from QA or programming, Cain has also had some very good ones that started out wanting to be producers.
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That last bit can also apply to Bloodlines 2 and its very pessimistic reception.
