[miamicuse]

OK I don't think these exposed splices are kosher...

Those are 120V line voltage lights.

 

[joed]

no they are not. They need to be in junction boxes.

 

[FrodoOne]

If the voltage supplied to the lights is "extra low voltage" (to use the IEC term) of (say) 12 V, there isn't much of a safety consideration, although the set-up is quite ugly.

If the voltage of the supply is 120 V, the connections and wiring are both inadequate.

 

[Wiredindallas]

This is why I hate and never use puck lights. There is no way to avoid exposed wiring even if it is safe low voltage.

 

[miamicuse]

may be it's easier (and less work) to rip all that out and redo it with LED strip lights?

 

[joed]

The NM cable will still need to be terminated in junction boxes. Only difference is you install a receptacle to plug in the LED instead of a blank cover to close the connections.