I read the first sound laser (or SASER) was made in 2010 here. But if we're talking about the state of the phonons emitted then we could say that any sound created by a planar vibration has a unique wave vector $\vec{k}$ and its phonons are spatially coherent.
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The papers described in the report you've linked to demonstrate examples of sound amplification by spontaneous emission.
This is independent of the characteristics of the waves that those source produce. As it happens, for sound (as opposed to light) it is relatively easy to create waves that have high spatial coherence and well-defined wave vectors $\vec k$ without using amplification by spontaneous emission.
However, that does not mean that sound with those characteristics, produced via other means, should also be called a 'saser'. This should be obvious -- it's no different to the fact that octopuses shouldn't be called spiders just because they also have eight legs. If it isn't, then maybe it's good to spend some time understanding the fundamentals of how lasers work.
answered May 11, 2020 at 15:03
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$\begingroup$ thanks for your condescendence Emilio, but you missed the point. I edited with bold letters so you can read. The question was about the terminology that is vague. I could tell you that it's not because we have " amplification by spontaneous emission" that we have a laser at the end. I was hoping for more discussion and not lame comparison with a octopus $\endgroup$– ceillacCommented May 11, 2020 at 15:55
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$\begingroup$ @borilla I'm happy to reconsider this text if any meaningful edits are made to the question's title. Otherwise this answer remains accurate. There may well be a meaningful question that merits more discussion in your original intention, but if you want that discussion then you do need to write the question text in a way that does not require this type of answer. $\endgroup$ Commented May 11, 2020 at 16:01