The other response pretty much nailed it.
Basic working knowledge of how code works on the web, and how data flows from Point A to Point B is a bare minimum in my mind.
Then you're often dealing with a data warehouse, BI tools and the modeling hell that comes with it, etc.
Beyond that, there is using code to improve performance directly. Speeding up page load times directly impacts SEO these days with Google. Knowing where and how tracking breaks (ad blockers, cross-device cookies dropping, messed up UTM params, cross-domain tracking setup, cross-channel attribution, etc.) and the million "gotchas" that come with any analytics platform is also quite technical.
Then outside of the tracking there's things like media and ad buying. There's some crazy work that goes into bid algorithms used by all the big search and display platforms.
The other poster's point about getting it into all the nooks and crannies of your marketing channels is spot on. Involving marketing and adding tracking to every single new feature is a requirement for product development. Linking all marketing systems under one roof and determining a SSoT is critical, but often Sisyphean, task.
In terms of a basic tools/languages list, I'd say...
- HTML, JS, CSS
- Whatever stack you're working on...so common ones probably have some PHP or RoR
- Google Analytics and/or Omniture, or some other solid analytics platform, as well as their respective APIs for dealing with events and other goodies
- Other pieces in the marketing stack such as data warehouses (Redshift, etc.), email platforms, CRMs, bid management platforms, ad servers, tag management systems, CMS's, etc. These all need to be linked together in an ideal world.
Feel free to ping me if you have any other questions. Contact info is in my profile.