Comparing your round trip Seattle to the Princess Cruisetour isn't an accurate comparison. There are a lot of variables to consider. First, are they even on the same cruise line? Even on the same cruise line different classes of ship, age of ship, popularity of itinerary, date of travel, how far in advance booking, and type cabin all can be factors.
I highly recommend you talk with a cruise oriented travel agent about your Alaska cruisetour. Princess has many different combinations of cruisetours. Price can differ by the type of transportation used (bus, or rail), types of accommodations, and the number of nights at each destination. ie: 2nt-Denali, 1nt Fairbanks,1nt Anchorage, could be cheaper than 2nt Fairbank, 2nt Denali. etc. A travel agent can sort it all out for you.
Having everything booked as a complete package will be less stressful and a time saver.