UPDATE:
As I expected, web check-in failed with the following message:
Airport Check-In Required
Our records indicate you are traveling to an international destination on another carrier. Please proceed to the airport and present your international travel documents to an Alaska Airlines or Horizon Air Customer Service Agent for check-in.
To navigate the rest of the site, use the tabs above or click the logo for the home page.
Code: -8369
FormName: UCSystemLevelError