Essentially, you get what you pay for.
The cheaper ones (e.g. vinyl) work okay to block wind, but are very susceptible to wear and tear, may rip, may pull off the door entirely, leak if your floor or sill is uneven (they can conform but only a little), and only provide a wind block rather than true insulation. Also, they leak around the edges. But they are generally under $5, so if you don't care too much, you can just replace them every 5 years.
The neoprene and foam ones are generally more expensive, and will conform better to an uneven floor (like most floors). Less abrasion resistance, though, so they wear out faster.
Ones like that silicone one create a bubble of dead air between in and out, providing actual insulation in addition to stopping air travel.
All of these designs depend on the screws holding the stop against the floor, so strong winds may defeat them. This means they drag as you open and close the door, and eventually they wear out. They may also get hung up on carpets or the like.
An alternate design mounts to the bottom of the door, rather than the inside edge. These include a U-channel usually made of metal, and multiple 'sweeps' to create that long bubble of air. They are adjustable, but require you to have more clearance beneath your door--essentially your door has to be hung with them in mind. They work great, and they protect the bottom of your door from rot provided you caulk the outside edge well.
At the high end there are also spring-loaded systems. They are U-shaped channels and also have a spring-loaded gizmo that presses down against the floor when the door is closed but pulls open when the door is ajar. It sounds great but I have no idea if they work--too expensive for my needs.
Though the crack is diagonal it looks relatively straight. In this case I'd take a piece of wood the approximate thickness of the crack at it's widest, cut it to length and then taper it so that it fits quite snugly - you should have to use a mallet to tap it home. Don't worry about the thickness too much - but obviously it should be fairly close.
Once this fits use wood glue to bed it in and fill the imperfections, though you might get a better finish using wood filler for this. Basically put more glue in than you need so it gets squeezed into every nook and cranny. Clean it off before it sets, then leave the repair to set.
Once set use a chisel to remove the excess from both sides of the panel and finally sand to make it flush with the panel. Fill any remaining (and hopefully small) holes, prime and paint.
By making the fit tight you minimise the chances for it to move, and therefore crack, further.
Best Answer
Yes, you are correct that the slot may be used for insertion of kerf-type weather-stripping, either for the Z-compression-foam shown in your link or a simple "flexible bulb" plastic edge that is positioned in the gap by the blade edge in the slot and compressed when the door is closed.