The phrase "to continue that dominance" means to maintain or uphold a position of power, influence, or superiority that has already been established. Full definition
Still, with no competition in its class, the automaker is poised for continued dominance of the «large families who love hybrids» market. (hybridcars.com)
Three points is all they need to continue their dominance in the league. (goonerthoughts.com)
I'm not worried at all about seeing continued dominance from the 3DS, but with 2013 being such a great year for the platform, developers have a lot to live up to! (nintendoworldreport.com)