The source you linked is third party text, so it's completely up to the GM. The GM may also have modified the ability to meet the needs of his game.
If I were running it as written (i.e., as if it was in a Paizo-published source), it's simply total concealment. This would be sufficient for a Stealth check, which would be sufficient to deny opponents their Dexterity bonuses to AC. Without making a Stealth check, though, other characters would be able to track the creature's movements just fine. Basically, it functions much like a shadowdancer's Hide in Plain Sight.
Like Blaphers said it gains total concealment not invisibility.
Invisibility also confers total concealment along with other benefits that this ability would not give the rat.
That being said total concealment does not mean that the opponent is automatically denied their dexterity to attacks from the creature in the concealment. That would require stealth or a number of other ways to create that situation. Concealment just allows for a chance to use Stealth, etc.
Also, try and keep flat-footed and denied dexterity apart as they really are different situations. A character that cannot be caught flat-footed may still be able to be denied their dexterity in certain situations.
Note this is not a standard dire rat, as the tread title implies, but a variant creature. Standard dire rats do not have the named ability.
