The black wire coming in from the top and attaching to the right terminal of the left switch is likely the "incoming" hot wire from the panel or upstream somewhere.
The black wire on the left side of the left switch is the switch leg for one receptacle, and the black wire on the right side of the right switch is the switch leg for another receptacle.
The second wire connecting the two is simply there to bring electricity from the left switch's hot to the right switch. It is possible to daisy chain switches this way, or one could use a wire nut and two tails to connect to the switches (this is how I would do it, easier to rewire later if e.g. a switch fails or if you want to swap one for an upgrade like you are now).
Note: your question says there are neutrals going to the switches, but these appear to be black (hot) wires with white paint on them.
The Z-wave switch appears to require a neutral based on images of the product, so you will need to tap into a neutral.
Be careful that you are using a real neutral and not a hot with white paint on it (this is one reason to put painter's tape over receptacle boxes when painting).
The neutral must be on the same circuit as the hot being switched. If only one circuit feeds this box there is no problem.