The article here gives the argument for the "just for show" explanation. The points it makes are reasonable. But here's what it overlooks.
Trump's missile attack on Syria was part of an ideological attack on Russia that is arguably far more consequential than the admittedly minimal physical damage inflicted on the Syrian airbase by the missiles.
During his entire election campaign and even just days before the missile attack, Trump's strongly argued message, backed up by his administration and even his UN Ambassador, was that there was no reason to be war-like against Russia and that there was no need to remove Assad from power.
This was the anti-war ideology that infuriated the warmongering elements such as Hillary and McCain et al, but which garnered Trump enormous support from ordinary Americans who are sick and tired of perpetual unnecessary warmongering.
But suddenly, inexplicably (the evidence is strong that Assad did not launch the chemical weapon attack), Trump and people like his UN ambassador, do a 180 degree turn on the fundamental anti-war ideology; they declare--with no evidence!--Russia to be enabling the use of chemical weapons of mass destruction and using military power to maintain a MONSTER (Assad) in power, who must be removed for the sake of all that is good and decent. And if Putin is the kind of evil man who maintains a MONSTER in power in Syria, then it follows that he is certainly guilty of all the other crimes ascribed to him in Ukraine, and we must use all the force it takes against the Evil Russian dictator. Suddenly the anti-war ideology is replaced by the pro-war ideology based on nothing but lies.
I believe that the American Billionaire class wants the pro-war ideology to prevail, because this ideology is what legitimizes the military-industrial complex that enriches the upper class at the expense of everybody else. It's the pro-war ideology, the fear it induces and the consequent willingness to obey our upper class leaders that it creates, that the Billionaire class requires, not the actual firing of missiles or any particular amount of military destructiveness.
The argument that Trump made this KEY ideological turnaround for the reasons advanced by the "Just for show" thesis--to improve his ratings and get the Hillary and McCain crowd to stop accusing him of being Putin's puppet--is not persuasive. Trump's right-wing talk radio host supporters totally oppose his missile strike on Syria and fear he's caving in to the warmongers. Rank and file Trump supporters are confused and torn between opposing the missile strike versus giving Trump some benefit of the doubt. Most of the Democratic Party people who were for Bernie also reject the pro-war ideology and thought the only good thing about Trump was his opposition to it. Trump has sacrificed one of the main factors that made him at least seem like a genuine populist.
As for the missile strike showing the Chinese president that the U.S. was tough, there are lots of ways Trump could have done this other than by doing a 180 on his anti-war ideology.