What is this red mark that resembles a net bridge in circuit diagrams?
The clue here is the signal names: x_P and x_N. 

These traces are balanced differential signals, which have a specified impedance.  The red symbol on the schematic is indicating that these are required to be routed as a differential pair. This means calculating a geometry to establish the required impedance, and then the design software will try to maintain that geometry when the pair is routed on the PCB. 

These are high speed HDMI signals, which absolutely require proper routing to maintain signal integrity. They should also haved noted the differential impedance required as well: 100 \$\Omega\$ for HDMI.