I think it's evolving thanks to greater tri-services integration (e.g., Project Vision and RAMP, Space Command, etc). So, the tri-services could be building towards common goals, but can be responsible for domains they're best equipped to handle. With its investments in air defence over the years, it seems the Army is confident it can support the HQ-9. In fact, this sets the precedent for the Navy to also induct a long-range SAM down the line for its surface ships.
The alternative is that the tri-services have revised the coverages they're responsible for ... e.g., maybe the Army and Navy can go up to 150 km range and 60,000 ft altitude, but the Air Force owns everything above that plus stuff like BMDs, satellites, etc. So, the PAF is becoming more of an 'Air and Space Force'.