Putting aside all the controversy of LENR (low-energy nuclear reactions, the official name for cold fusion) and assuming that the theory actually results in usable tech (for once), the first line of the NASA article hints at where a device's power density would be competitive:
> "A team of NASA researchers seeking a new energy source for deep-space exploration missions"
which tells me that a theoretical device would be a replacement for current RTGs [1]. Low but consistent power for niche applications.
But in general I wouldn't get your hopes up. The higher-energy types of fusion power are far more promising for world-wide civilization-powering clean energy.
[1] https://en.wikipedia.org/wiki/Radioisotope_thermoelectric_ge...