Finally stung you, did I? I really don't have to prove anything to you. But as a matter of politeness, I'll answer the question.
Actually, a transaction point is slightly subjective. In transaction-oriented systems, a transaction point is the smallest unit of meaningful activity in a sequence of activities leading from the start of a process to its end. It is "one small step among many." I.e. in "The journey of 1000 miles begins with a single step" the individual steps are transaction points. Subjectivity comes into play because of the word "meaningful." If you have meaningless activities then they are technically not transaction points. Sort of like trying to explain things to you, sometimes, Adam.
I've been around long enough to hear other methods of process and project analysis including decision points and action points. People always look for ways to analyze things. Sometimes it works. Sometimes the type of analysis is a fad that dies down when people realize it doesn't help them. I recall using this concept when doing software cost estimates. The problem with doing so was that you had to almost write the software in order to estimate its cost - in other words, leading to a two-pass algorithm to get answers that were needed in a single, short pass.
By the way, "clicking a button on your screen when you are running software" is an incompletely specified example. I can click a button on a non-active section of my screen. That is NOT a transaction point because it does nothing.
Also, "pressing any key when your cursor is inside the search box" is also an incompletely specified example. If the only key I press is either ALT or CTRL or SHIFT (each of which qualifies under the concept of "any key") then I have again done nothing. By the way, that would still be a transaction point for the device driver of your keyboard - but not for the Google search box, which is what you specified.
The activity has to be MEANINGFUL and two of your examples incorrectly were defined to include non-meaningful actions.
Is that smart enough for you, Junior?