What is a (side) current alarm?
I think that the text is badly typed. If we change

R_IS: Forward drive - side current alarm output
L_IS: Reverse drive - side current alarm output


to 

R_IS: Forward drive-side current alarm output
L_IS: Reverse drive-side current alarm output


it implies that the alarm is on the "drive-side" of the board as opposed to the control side.

The BTS7960 datasheet says:


  The status pin IS is used as a combined current sense and error flag output. In normal
  operation (current sense mode), a current source is connected to the status pin, which
  delivers a current proportional to the forward load current flowing through the active high
  side switch. If the high side switch is inactive or the current is flowing in the reverse
  direction no current will be driven except for a marginal leakage current IIS(LK). The
  external resistor RIS determines the voltage per output current. E.g. with the nominal
  value of 8500 for the current sense ratio kILIS = IL / IIS, a resistor value of RIS = 1kΩ leads
  to VIS = (IL / 8.5 A)V. In case of a fault condition the status output is connected to a
  current source which is independent of the load current and provides IIS(lim). The
  maximum voltage at the IS pin is determined by the choice of the external resistor and
  the supply voltage. In case of current limitation the IIS(lim) is activated for 2 * tCLS.