Pathogens aren't animals, so the mosquito is the one counted.
They don't count humans the same as other animals, instead, they count homicide/war (intentional killing), and you can just consider it a point of reference. Are you going to count accidents? Suicide? Anything that can be traced to human decisions? Anything that can be traced to human biology?
Any way you count humans, it just isn't going to be equivalent.
In the chart, the humans vs. mosquitos are not fairly comparable.
First - if you're going to say 'mosquitos kill humans because they transmit disease' and then include humans for a completely different reason (i.e. homicide) makes for an odd comparison.
For example, what if human transmission of the communicable disease results in some massive amount of death, which could very well be the case?
Second - mosquitoes are carrying a lot of otherwise benign things, which most people recover fine from. Possibly things like the flu. Well some people die from the flu, but very rarely. So I'm not sure if the fact it was communicated by a mosquito or something else makes sense.
Maybe inanimate objects, like the door handle to your public building, contribute more to basic pathogen spread, like the flu, in which case again, that would put things in context.
It's a tricky thing to compare lions attacking people to mosquitos that happen to spread in some cases, some minor thing that in may have rare deadly consequences.
Well I said elsewhere that they should probably skip the humans since it is so different, but I got pretty well downvoted.
Malaria is almost exclusively spread by mosquitos, so there is a certain logic to saying "mosquitos kill a lot of people." But you are right that most times you are bitten by a mosquito, it is nothing but a minor annoyance. It's a bit different from a lion.
Some people include deer in such charts, because people die by crashing their cars into deer. But that is pretty different too.
Humans are also vectors for pathogens, we just don't count them as such.