> it doesn't sound very convincing
That's because it's not a strong conclusion. It's a "better than the alternatives" hypothesis. Repeating my tldr above "they don't know it's alphabetic".
> doesn't bring any EVIDENCE .. some morphological characteristics of the inscriptions
I'd say the "morphological characteristics of the inscriptions" count as evidence and I'll just recap everything linked that I think counts as evidence: the graphemes include several repetitions even with only 12 signs in total; they don't resemble cuneiform at all; they have a weak resemblances to some Egyptian glyphs but weak and Egypt didn't have these clay cigars; they have a weak resemblance to some Indus glyphs and (later) Byblos glyphs but again weak; they don't appear to be numbers, potmarks, etc.; but what they do strikingly resemble is later alphabetic signs, to the point where the author, one of the foremost experts on Semitic epigraphy, really wanted the dating to be wrong.
Now the blog post doesn't go into much detail on these items but Schwartz's 20+ page 2021 paper (I had no trouble getting a free, legal copy) does (not always a lot more detail but also covers more possible alternatives). But, like the blog post says, the case Schwartz 2021 makes is still extremely cautious and he basically concludes that we just have to hope we can find more examples to confirm what kind of system they are from, and to increase the chance of deciphering them.
> Egypt didn't have these clay cigars
Sometimes a cigar is just a cigar.
I'll escort myself out now...
How is it better than the alternative "we have a set of symbol and we don't know what it means"? I really think there is a merit in saying "with this sample size, every theory we put out has low confidence level".
With 12 signals in total, it's very hard to show patterns that are in line with an alphabet. I don't think that with this sample size you can make a very strong claim that the chance that this is an alphabet is higher than the chance is that these symbol serve any other kind of purpose (including being a non-language). The main claim seems to be that repetition (what kind? I'm a quite disappointed the blog post has no transcritions, considering it's just 12 symbols we're talking about!) makes the chance that this is an alphabet higher. The rest of the claims (it doesn't resemble cuneiform, doesn't seem to be derived from hieroglyphs and doesn't seem related to any other script) are meaningless. The resemblence for later Canaanite alphabetic signs is interesting, and could probably be more convincing if we had a larger sample size.
So in the end, if we are convinced by these claims, we're basically saying something like "We have at most 1% confidence for every other theory, but we've got 2% confidence that this is an independent development of the alphabet that may have inspired the Canaanite alphabet we've seen 500 later". Higher confidence that is still far below the threshold doesn't cut it.
Now, I'm pretty sure the original article did not put the theory in these terms, but the headline is somewhat sensationalist, and the way it was picked up in newspapers is even worse, for instance:
Scientific American: World's Oldest Alphabet Found on an Ancient Clay Gift Tag
Stopping the press from misreporting science is a bit like trying to stop space rockets in midair with your bare hands, but even "Evidence of oldest known alphabetic writing unearthed in ancient Syrian city". The popular understanding of the word evidence is assumed to be "hard" evidence by default, not a weak evidence that bumps up the probability of a certain theory a little bit more.
I'll actually be quite excited if this turns out to be truly an alphabet encoding a Semitic language (it opens a lot of interesting questions and possibilities), but I'm not holding my breath for it.