The word reactionary hails from the French word réactionnaire, which was coined during the French Revolution. Looking at the pages you scanned, they're using these words in the context of the European order that emerged after Napoleon was defeated. For that period it's not "surprisingly leftist" to describe the Bourbons as reactionary, it's so common it's almost a cliche. I also doubt many historians would bat an eyelid at seeing a world history textbook pithily describe Louis Philippe's rule a "dull bourgeois monarchy" or that calls certain regimes "illiberal and oppressive". Consider whether it actually sounds particularly leftist to describe Saudi Arabia as illiberal and oppressive?

These terms have certainly been picked up and bandied about in left-wing rhetoric, which is probably where you have encountered them, but there are contexts in which they are useful adjectives for historians of almost any political stripe. Granted that they can't be considered completely neutral terms, but that's mainly because they are an intolerable insult to French royalists and Russian tsarists.