Yes, the original sentence is grammatically correct. Here’s why: The phrase “by pushing the end against something” explains how someone puts out a cigarette. The word “pushing” works as a gerund here to show the action. If you change “put” to “putting” like this: “The word ‘stub’ means putting out a cigarette by pushing the end against something,” it changes the sentence’s structure and meaning slightly. The original sentence is clearer and sounds more natural in formal English. Stick with it!

The first sentence in your question is grammatically correct. Typically, definitions are phrased using the same grammatical structure as the word they define. E g. Eat means consume food Ate means consumed food Stub means put out ...