Complex sentence: Swalwell was able to contest Stark after the primary due to a new primary system in California, under which the top two vote getters advance to the general election, regardless of party affiliation.
Split into simpler sentences: Swalwell was able to contest Stark in the general election because of a new primary system in California. Under that new system, the top two primary vote-getters (Stark and Swalwell, in this case) advance to the general election, regardless of party affiliation.