I compared the route they screenshotted and apparently the only reason TripDelta come up with a $150 cheaper one-way option ($302 vs $455) is by flying Spirit from OAK to LAX with a 9 hour layover. Kayak probably assumes that layover is excessive and filters it out. Because really, if you're that desperate to save funds, just take Greyhound to LAX.
And if you book round trip, returning a week later, it's $779 on Kayak and over $1086 on TripDelta. Plus Kayak will also give you the probability that prices will drop in the next 7 days.