What skillsets do you look for in growth product managers?

Good at data and insights

Ability to identify growth opportunities

Ability to quickly test hypothesis

Ability to hack through and come up with exciting ideas (big & small)

Relentless focus on execution & results

Good at product design and User experience

Strong team player as this is a heavily cross functional role

Off the top of my mind...

1. You MUST understand the difference between artificial growth and sustainable growth. For example, if you ran a publisher site like CNN, and your growth PM idea was to grow revenue by plastering the entire page with Ads, that's not sustainable. You might see revenue initially jump but your users will eventually leave your site. 
2. Data-minded - you have to be comfortable with data and have the curiosity to seek more data. 
3. Understanding digital marketing is a plus but not a must. You should know some common business sense like if your cost per acquisition is more than the LTV that the user brings, then you have a problem. 
4. Being able to work cross-functionally - Growth PMs often find that there are growth opportunities beyond the product they own. Therefore, they have to be good communicators and able to work with other PMs to get work done. 

The same skillsets as for PMs: be humble, be great at communication with anybody - and especially business! - , and have the ability to develop a product sense.