If the inputs are with pull-down resistors, then the schematic is correct.
Normally input is pulled down to 0V by the on-board resistor. Input state is 0.
When +5V is connected to input, input goes to 5V, and changes state to 1.
The 1k resistor is there to limit current if the alligator clip is accidentally
connected directly to ground. The input has normally enough Rin (input
resistance in this case) to limit current to reasonable value. The circuit would
work even without the 1k resistor (current limited by input Rin), but it is a
good idea to have it there for safety.
The 1k resistor must be sufficiently smaller than pull-down resistor (input voltage
is voltage from divider of pull-down resistor and 1k resistor), which it appears to be.
Often pull-down resistors are 4k7 or 10k.