This is not a soft spot per se, it is a crack. Soft spots are where the skin has not been broken. Yes it may be soft but your biggest worry is the broken surface that is damaging your ski from the inside out. Water will be filling the core and migrating behind the waterproof gelcoat, a recipe for disaster in the longer term.
Yes a repair is 100% needed! First thing is to stop water from getting into the ski, good quality Duct tape is essential until you get it repaired.
As for repairing, it is essential to be dried out 100% before you can do anything. Sanding the gelcoat away to the first layer of fiberglass wherever it is soft will help this process. Gelcoat is your waterproof layer and will inhibit this from happening, trapping water behind it. Be very careful not to apply much heat as you will cause a lot of damage. I usually help the process along by taping lots of tissue paper over the fiberglass which draws out the water, obviously you have to get all free flowing the water out the ski that is in it otherwise every time you move it, it will contaminate the crack again with water, this can however take weeks to get all the water out. Don't laugh I get skis still full of water, not drips but litres.
As for the repair I use epoxy as I know it will bond even when not 100% dry whereas styrene based resins will not bond to anything slightly damp.