Alaska had planned to move from their own application process to something they called a "talent pool" using Smart Recruiters to filter all of the applications (and, to the chagrin of many, to try to direct applicants to Horizon). Somewhere along the line, they discovered that just wasn't working the way they thought it would, so they returned to their old in-house application process.

The answer to your question is to use the Alaska careers page. To the best of my knowledge, they aren't doing anything (nothing that will get you hired, anyway) with Smart Recruiters at this point. It can't hurt to do both, but it probably won't help.