Connecting phone using copper power wires
If those two terminals that you show in your picture are the only connectors, then you should be fine. The intercom specification indicates that it is a wireless video system, so all device communication is probably happening somewhere on 2.4 GHz. Those screw terminals, and the fact that there are only two terminals, along with the power requirements being listed, are pretty good indicators that those wires carry only power. If it carries only power, then your normal house wiring will carry power just fine. If the video signal is carried by the wires, then they probably would be using the cable as network wiring and the house wiring might not work.

A caveat: The twisted wire that they specify will give you some noise rejection that the regular untwisted house wiring will not. If your intercom design is somewhat marginal, then you may have random interference. You could mitigate this by putting some ferrites around the power wires near the intercom, and possibly twisting the two power wires in the run.

Note that this is all independent of any building code requirements your building may be required to meet.