Based on your route, sounds like Horizon/Alaska Airlines. You will be OK. And as mentioned in previous reply, gates are easy to maneuver. Horizon has most of their gates in one general area. They have covered tarmac pedestrian walkways leading you directly to your plane..very simple. Safe travels!
It's pretty easy to get around SeaTac. All one terminal. If you are on the same airline the gates will be in the same wing. The only thing that may slow you down is that fact that the smaller aircraft sometime deplane on the apron and require a bus ride to the terminal.
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