A dislocated knee is a catastrophic injury requiring immediate arteriogram and other emergent treatment. I have treated a few, and saw the follow up of an all army track athlete who lost his leg following a poorly diagnosed knee dislocation. A knee cap dislocation (patella) is a much less severe injury, that can rehab in as little as a few weeks depending on the patient. I think that injury is not likely in the scenario I saw.
Most likely for this, based on the two different angles I saw , is LCL injury and/or meniscus injury.
Sometimes the ligamentous injury is not too serious even though it is immediately very painful, and can have a short recovery. Even with a complete tear of the LCL, with the proper bracing and rehab, I would expect Carter to get through the tournament in similar fashion to Jason Nolf, if there are no untoward complications.
With a small meniscal tear there could be the same result, although in that case there can be more episodes of knee giving way due to the meniscus catching in the joint intermittently, which is a little less predictable than the course following a LCL injury.