A hikiotoshi is generally performed while backing away, giving it a special angle of force to "pull" the person down. A tsukiotoshi is more of a thrusting type of motion, using more raw force to twist a person down while pushing.
This totally unrealistic "lifting a rikishi up before tossing him on the ground" obviously doesn't have a perfect parallel in real sumo wrestling, but I think the author was trying to convey a greater sense of power by indicating that the finisher ends with a thrust rather than a pull.