The problem with Li-Ming is not so much her damage as how it is delivered. Both Magic Missles and Arcane Orb are exceptionally powerful nukes on short cooldowns. Missiles especially since they are cheap and spammable throughout the entire game. It is not reasonable to expect the enemy team to avoid every skillshot Li-Ming throws when she tosses them around like candy.

KT's Fury of the Sunwell does about as much damage as Ignite did, but it is not nearly as good. This is because the second flamestrike rarely hits the same target twice, tending to either hit different targets or act as area denial.

Chain bomb is much the same, if you ignore KT's ability to instantly detonate a living bomb. You could argue that the latter part of that talent is overpowered and needs to be either removed or delayed. The point is that all the damage is spread out and only bursts a single target under special conditions.

Yet another example is Jaina. Tons of AoE which can be used as burst, but only if Jaina puts herself in harms way. The "Jaina flank" is a high skillcap strategy used to blow up a backline target. If you are unsuccessful or your team does not follow up Jaina ends up out of position.

All of Li-Ming's damage emulated KT's Ignite of old. Low resource burst that can be used from a range that does not put Li-Ming in danger. Every 3 seconds Li-Ming has another chance to chunk a target magic missiles, and every 10 seconds is an opportunity to delete a target altogether.

I agree that the gif is misleading. Getting in close range with a mage is always a gamble. If they know how to execute a combo then the best you can hope for is mutually assured destruction. The problem is that Li-Ming's destructive potential does not drop off no matter what kind of positioning or counterplay you utilize.