First of all, it is not clear why this automorphism is worth writing a paper about. The impression the authors create is that it is some sort of curiosity (I am not disputing that the algebra itself is important). Second, the authors themselves mention that this automorphism can be obtained without explicit computations and from the fact that this algebra can be realized as a subquotient of an affine Lie algebra with a diagram automorphism. At least, they should have explained how this is done rather than making a remark that it is possible to do so. Third, the paper is written in a rather cavalier way (that is, a bit too informal for a mathematical text). Arguments boil down to "This is the presentation of our algebra in terms of generators and relations and they are clearly preserved by the automorphism in question". There are also some minor mistakes (like a subalgebra is called a subgroup).