Actually, in all likelihood, rest will not help Kawhi's injury at all.
I’m not a doctor but played a lot of ball and have had quadricep tendinopathy.
Someone is “able” to play through quad tendinopathy but it is uncomfortable and seriously aggravates the tendons. Usually, when tendinopathy occurs, it's because rest wasn't taken initially and the injury has turned into something akin to chronic inflammation (but inflammation isn't actually present on the cellular level).
I learned, after the fact, that in playing through my tendinopathy, I turned a small injury that could have been treated with two weeks of rest, into an injury that required two years of rehabilitation and treatment. Even with treatment, I was unable to squat down to tie my shoes for the better part of three years.
Essentially, it’s an overuse issue in which the athlete has had many micro-traumas to the tendon, and as such, their body begins to dump type-3 collagen (weak scar tissue) in unorganized bundles atop the injury sites. Our tendons are made of well-organized bundles of type-1 collagen, so this is problematic. Imagine cutting a bunch of incisions into a piece of paper and then handing that piece of paper to a child and asking them to use that tacky white school glue to patch the holes — that’s sort of what’s happening within the body during tendonopathy.
As rest alone will not heal this issue, to combat the body’s response, most physiotherapy consists of eccentric loading (lowering weights very slowly) and not performing the isometric contraction (lifting the weights up). For patellar tendinopathy this would be something like wall-sitting and holding your weight on your injured leg, and then standing up from the wall-sit with your healthy leg. This more-or-less teaches or shows the body to once again deposit the collagen in tight and straight bundles.
This is problematic because the athlete needs to load to that perfect balance where they are achieving the necessary resistance/load to incur healing, but not so much resistance/load that they’re aggravating the injury. As such, the healing really feels like 2 steps forward one back. It’s a delicate affair.
Eventually, the athlete has to slowly re-introduce jumping, running, and other explosive movements in increments so as to not completely ruin their tireless rehab efforts. It’s difficult and frustrating for the average athlete, and likely even more so for a highly motivated athlete like Kawhi.
So, while he may be feeling minimal pain and have full functional movement at this point in his recovery, physiotherapists and doctors need to be very very careful not to rush him back. He'll also need to correct his biomechanics that caused the issue in the first place to ensure that he’s not re-aggravating his injury again, as once it becomes chronic, it could plague him for the rest of his career.
So, yeah, it’s really a touch-and-go scenario that is more of an active recovery than you may believe. But with the trainers and professionals he has access to, he’ll likely clear it up and never have to deal with it again. In my opinion, it's wise of him to sit and avoid aggravating the issue.