Is fermented food or drink halah?

Drinks and foods that are fermented and contain some alcohol concentration are of two categories:
First:
Where the alcohol concentration in the drink is high, in such a way that drinking a lot of it will cause intoxication, this is khamr, no matter what it may be called, and it is prohibited to drink it in small or large quantities, even a single drop.

It was narrated that Ibn ‘Umar (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Every intoxicant is khamr and every intoxicant is haraam.” 

Muslim 
It was narrated from Jaabir ibn ‘Abdullah (may Allah be pleased with him) that the Messenger of Allah (blessings and peace of Allah be upon him) said: “Whatever intoxicates in large amounts, a small amount of it is haraam.” Abu Dawood and Tirmidhi

Second:
Where the concentration of alcohol in the drink is minimal, in such a way that it will not cause intoxication no matter how much a person drinks it. This concentration has no effect, and this drink is halaal because the basic principle with regard to all drinks and foods is that they are halaal, except that which Islam prohibits. There is no evidence in Islam to suggest that the mere presence of a small concentration of alcohol in a drink – no matter how small it is – makes the drink haraam. Instead, the hadith quoted above indicate that the reason for the prohibition is intoxication; therefore, whatever drinks cause intoxication is haraam, and whatever does not cause intoxication is halaal.

Based on that, if this food asked about does not cause intoxication, no matter how much a person eats of it, then it is not haraam.