Ever since WWII it has been more and more difficult to define our “wars”. The line tends to get blurry when the President doesn’t have to consult Congress before sending in troops.
However, when you are bombing a nation, and occasionally using ground troops, then I think it is defined as a war. Just because we aren’t trying to overthrow a government (i.e. Iraq and Libya) doesn’t mean we aren’t at war (i.e. Iraq and Afghanistan). Of course this means that we are at war in Pakistan, just at a lower intensity.
Oh sure, there will be people who deny it. But consider the lessons of history on how easily bombing a nation can turn into a broadening war (i.e. Vietnam, Laos, Cambodia).
There are many reasons why it is important to acknowledge how many wars we are engaged in. Not the least of which is so that it focuses the public on what our government is up to, rather than ignoring our foreign policy disasters until there is blowback.
This means that we must pay attention to what our government is doing in Yemen, and most of all, Somalia.