What are leaders called whose personal style makes them more task- or goal-oriented and less concerned with people's feelings?

Those leaders are called "Instrumental leaders".

There are ordinarily two sorts of leadership: instrumental and expressive. Instrumental leadership spotlights on accomplishing objectives. An instrumental leader is one who leads in methodology and usefulness. This leader sorts out procedures, set tasks into movement, and directions work with different representatives. This sort of pioneer utilizes all assets accessible to accomplish exceptionally specific objectives.