There are many ways to create new creatures in D&D 5e, one of which is animate objects which gives the player full control of the creatures when he/she uses a bonus action:
As a bonus action, you can mentally command any creature you made with this spell… You decide what action the creature will take and where it will move during its next turn, or you can issue a general command, such as to guard a particular chamber or corridor.
There seems to be no such language for a Beast Master's Ranger's Companion which instead says:
The beast obeys your commands as best as it can. It takes its turn on your initiative, though it doesn’t take an action unless you command it to. On your turn, you can verbally command the beast where to move. You can use your action to verbally command it to…
Does this mean that the beast is considered an NPC and is therefore under the control of the DM or is it under the player's control from some rule I missed?
In practice, yes, unless the ranger's unable to command it.
Yes, the player of the Beast Master Ranger does effectively control his/her animal companion most of the time.
As you quoted:
It doesn't take an action unless you tell it to. It doesn't move unless you tell it to. It can use its reaction freely (e.g. for an opportunity attack), though it presumably would only attack a creature that you'd expressed hostility towards or vice versa, or one which is hostile to the animal companion itself.
In practice, this means that the Ranger player does indeed control what the animal companion does. There's no specific range restriction in which the companion can be commanded, but unlike Find Familiar and Find Steed, there's no telepathic bond between a Beast Master Ranger and their animal companion - so the only way to command the animal companion is verbally (or maybe with gestures, though I don't think there's any RAW description of that).
The 1st-level spell beast bond (EEPC, p. 150) does make telepathic communication possible:
It's a Touch-range concentration spell that lasts up to 10 minutes.
(Beast sense (PHB, p. 217) is another spell that essentially lets the animal companion function like a familiar; it's a 2nd-level concentration spell that lets you see and hear what a willing beast sees and hears, for up to an hour or until you use an action to stop doing so.)
In other words, the player controls the animal companion as long as it can hear the Ranger's verbal commands, or as long as it's within line of sight if the Ranger casts Beast Bond on it.
If the Ranger falls to 0 HP (or otherwise falls unconscious), Mike Mearls unofficially says he would rule as a DM that "I'd let it protect and aid ranger" - after all, the animal companion does have a special bond with the Ranger.
In addition, he replied to a question about what would happen to the animal companion if the Beast Master Ranger actually died as follows:
Again, though, this is Mike Mearls' personal opinion as a DM, not an official declaration of the rules.
In summation: in play, the Ranger's player effectively controls the animal companion as long as the Ranger is able to somehow command the companion. The DM would likely control the animal companion in most other cases.