The power is unclear about whether or not it can be used for Grab attacks, which is probably the source of your confusion, but that's actually irrelevant to your question. Though I will note that grabbing someone just by the throat should be considered a Fine Manipulation, and require the Precise extra.
The real barrier to "force chokes" is the lack of the Chokehold advantage. Without Chokehold, the character has no mechanic for initiating strangulation. Suffocating foes requires moving them into an environment they can't breathe in (water, wet cement, vacuum of space, chamber of car exhaust, etc.).
Using a Hero Point to power stunt a Precise & Chokehold version of Move Object would be a perfectly reasonable power stunt for most descriptors, sacrificing one rank of the power to do things not normally possible.