How does Product Marketing get involved with alliances, partnerships and marketing the integrations of a product with another product?

Yes, 100%. That can be it's own role on a product marketing team, especially if you are building a platform and have a large partership ecosystem. Marketing tech is a good example of this. Partnering with numerous other marketing tech companies can be your growth strategy, that's how a lot of companies got their start (including Privy). 

Also, integrations can be a success factor for your customers. Meaning you might realize customers that integrate with Marketo, for example, are more likely to be succesful with your product (they use it more, upgrade or churn less). So then prodcut marketing's job is to help encourage customer to set up that integration.  

This essentially involves zooming out with the exec team and making sure the team is on the same page on the definition of "product". If you can get leadership to agree that partnerships, integrations, services are all part of the solutions offered, this job gets easier. The responsibility for partnerships sits in different departments, depending on the company structure. Sometimes it sits with product, and in other instances with sales/revenue orgs, or have its own team that reports to the CEO or CRO. Understanding their KPIs and aligning with their goals is the first step to getting involved with alliances. Make it clear of the value add you bring to the table from being able to amplify these partnerships.