That's a fascinating article, but doesn't really support your case? It's a survey, and includes various summaries of past studies, including:
The above studies strongly suggest self-awareness in bonobos, dolphins, and the bluestreak cleaner wrasse, all of which are social animals.
It appears that the ants used their mirror reflection to see the unusual blue dot and attempt to clean it. If true, this behavior would indicate self-recognition. Additional studies are needed to verify these findings.
The rhesus macaque was originally thought to be incapable of self-awareness, along with several other species of monkeys (Gallup, 1970). However, newer research indicates the contrary but only after significant training.
With regard to octopuses, it says Thus, concluding a lack of self-awareness based on their performance in a visual test may not be fully reliable. Further self-recognition tests, preferably modified to better suit octopuses, are suggested.
In another study The authors of both studies highlight the need for alternative approaches in measuring avian self-recognition.
The author states A basic level of self-knowledge is guaranteed in animals that pass the mirror test, but it is unknown if they possess advanced understanding of private mental states and also Another area of future research is whether self-recognizing, non-human animals can know their internal mental states such as emotions. A basic level of self-awareness is confirmed to be present in non-human animals that conclusively pass the mirror test, but it is unknown if this can be extended to include their knowledge of internal thoughts and emotions.
What the paper is actually talking about is the need for more research, and the difficulty of extrapolating from experiments about self-recognition, to conclusions about self awareness.