My four-year-old son asked me this right after Kiddush on Friday night (more or less verbatim):
Why do you say "Mitzrayim" in Kiddush every week? "Mitzrayim" is a Pesach word!
In other words, why do we refer to Shabbat as "commemorating the Exodus from Egypt" (Wikipedia translation)? Isn't it really all about God's completion of Creation?
Tack-on question: Once you've established that Shabbat is linked both to Creation and to the Exodus, why is the terminology in Kiddush for these links slightly different? Shabbat is called "זִכָּרוּן לְמַעֲשֵׂה בְרֵשִׁית" - "a memorial to the deed of Creation" and "זֵכֶר לִיצִיאַת מִצְרָיִם" - "commemorating the Exodus from Egypt" (translations from Wikipedia; emphases mine).