The thinking is that muscle-building and strength training will improve what's called "peripheral insulin sensitivity". Remember that the effect of insulin is to get glucose out of the blood and into cells, where it can be used for energy. This works best with muscle cells.
People with T2D generally have a genetic or whatever predisposition to insulin resistance/insensitivity. One effect of this is that glucose doesn't work so well to get glucose out of the blood and into cells, particularly after eating. Building muscle can improve the situation, because insulin works best with muscles.
But the biggest issue for T2D's is often not this peripheral insulin resistance. Another and often more important effect of insulin resistance is to screw up the process by which your liver (mainly) manufactures glucose when you're not eating, mainly overnight.
The mechanism relies on insulin in the blood to tell it when to start and stop this process. If the liver detects insulin it assumes the pancreas has been producing the insulin to deal with glucose in the blood and so no more glucose is needed, so it turns the production off; and then turns it back on when it doesn't detect insulin, taking this as a sign that more glucose is needed to keep the brain etc alive.
When there is insulin resistance that detection mechanism can fail and the liver keeps churning out glucose over night even when it's not needed. The result is high waking BG levels. These don't have a lot to do with what carbs you've eaten; the liver can manufacture glucose from a bunch of different non-carb elements.
When you get fat build up in the liver it increases insulin resistance, so the detection gets worse and this over night over-production of glucose increases, making waking BG levels worse. At the same time, the fat can spill over into the pancreas, which over time suppresses its ability to make insulin. So you get a vicious cycle where the body produces more and more glucose with less and less insulin being produced to deal with it, leading to full-blown T2D.
If you lose enough weight you can clear the fat from your liver, improving its insulin sensitivity and reducing the amount of unnecessary glucose it produces, bringing waking BG levels down. Lose more, and fat can clear from the pancreas, increasing insulin production and so further imptoving the blood glucose situation and breaking the vicious cycle.
When you've gotten to "remission" via weight loss you'll see "normal" waking BG levels but still might have slightly elevated BG levels after eating, because you still have a genetic or whatever predisposition to peripheral insulin resistance. It's probably not a big deal, usually, so long as fat doesn't building up in the liver and pancreas again. But muscle building can reduce the peripheral insulin resistance, a bit.
From your numbers, you might be in that situation now. Non-diabetics can certainly see BG levels higher than 7.8 after eating, so there's nothing particularly "non-normal" about the numbers you report. But you might be spending a bit more time at those higher levels than the average non-diabetic and muscle building/strength training would probably reduce that a bit.
Bottom line: strength training is good for general health and will probably improve your insulin resistance and BG levels after eating a bit. But it's probably going too far to says it's "essential" for remission.
