Picked up certainly stand for "ammo (that) was picked". Of course, when it comes to game playing and (game) programming it depends on the "thought" of the programmer.
For example, there was an idea (I don´t know if they implemented as of today) of ammunition being picked up (pega) from fallen enemies, that is, the gamer would "scavenge" for arms and ammo, but then in (almost real scenario) it would be dangerous.
There is the ammunition that a gamer "gets" simply from taking the gun from a fallen enemy. Again almost irreal, since the enemy was spending ammo shooting agains the gamer and his unit.
Finally, there´s the use of ammunition (and health/life, etc) that the gamer go spending until he is almost out of it, he then stops (by pressing a button) and then "recharge". Picking up ammo would be the process of recharging here, and we could say in a more technical parlance of "resupplying". So, in that case - with "picked up ammo" we could talk about "munição reabastecida/resuprida".
Anyway, this is a guess of mine. Just a description of the process as I understood from reading around. I could be mistaken, of course.
Aside note: with music and games be aware that they kis (keep it simple) meaning they go succinct. So, leaving out the subject (it being implicit) is something usual.