An anti-slip, liquid management cover article for a flooring surface. The article includes a film defining a working face. A microstructured surface is formed at the working face, and includes a plurality of primary ridges and capillary microchannels each having a bottom surface. Each primary ridge is an elongated body having a length. A shape of a portion of at least one of the primary ridges is non-uniform in a direction of the length. The capillary microchannels facilitate spontaneous wicking of liquid. With this construction, the non-uniform shape establishes an elevated coefficient of friction at the working face as measured in multiple directions. The cover article minimizes the risk of pedestrian slippage, even in the presence of water or other liquids.