The activity score should include more metrics or be renamed to "Activity on LingQ Score"
I have always assumed that LinGQ's activity score measures activity on the LingQ platform. What else could it refer to? You are proposing to add self-reported activity to the overall score. One could argue both in favor and against that idea. You have made the case in favor, mainly that it would allow you to keep track of all your activity in the language, including what you're doing outside the platform. Others would point out that this would allow people to artificially inflate their scores. Some users have expressed their concern about this possibility in other cases because it permits "cheating" in challenges, etc.
I personally don't care one way or another. I don't pay any attention to most scores and particularly to such compound, overall metrics. On Lingq I only care about "words read" and "words known" and a bit about number of Lingqed words on a given day and that only in the first stages of learning.
In general, I would recommend not fixating on a single metric as a sign of progress. Remember GoodHart's Law: https://en.wikipedia.org/wiki/Goodhart%27s_law
Cheating your score
I think that the activity score reflecting your activity is what it should do, including activity off the platform, because most of us don't use LingQ exclusively to study our language(s).
I do agree that if the activity score affected other people, then it probably should not include manual statistics (or you should not be able to manually enter statistics if you are in a public activity score based challenge).
However, the only place the activity score is displayed publicly is on the forums (or on someone's specific profile). With that, I don't think that abusing the manual modification your activity score just for the sake of making it larger is of any benefit (unless you're looking to stroke your ego on the forums, which most people don't really want to do).
You make a good point here.
For me personally, I am not someone who is reflecting solely on the activity score to measure my activity in the language, I am someone who likes to look at a variety of stats to get a feel for where I'm at and where I'm heading.
Keeping track of my stats is by no means my most important activity in language learning, however, it does help me properly set goals and remind myself that I am indeed making progress. If the activity score were to accurately reflect your activity, I would have one more metric to add to the list.
Lingq is overall really great but activity score is not one of them. I find it slightly frustrating that you can't set your own targets. My daily french listening goal is set at half an hour, but I can easily smash that goal because listening is the least taxing activity, you can listen to anything almost anywhere doing almost anything.
Anyway for me it's not a big problem, I love statistics, Excel (google's the same I suppose), is pretty easy to use and that way you can completely tailor it to you needs.