Is this sump pump plumbing correct?
Plumbing is not correct.

You have a condensate drain that's been piped to the sump drain, and the check valve (black thing) is below it. But it would not work if the check valve was above it, either. (edit - perhaps that's just a coupling, not the common "check valve in a flexible coupling" I took it to be at first - does not change the answer.) The backpressure of the sump exit pipe to the exterior is evidently considerably higher than the small height difference to the top of the open tube getting the condensate.

Does the SUMP DRAIN operate normally if you close the valve? I'm assuming that when you say water runs out the top if you close the valve, you mean condensate from the furnace, not the sump drain water that you get when the sump operates if it's open.

If so, you just need to re-route the condensate to drain into the sump itself, not into the sump's drain line. Leave the valve closed, or cut it off and cap that. 

If the sump does not successfully drain to the exterior with the valve closed, perhaps the sump drain to the exterior is clogged, causing more backpressure than when this was set up, and perhaps it worked when the line was clear. Still Not a good setup IMHO, but perhaps it "used to work"...9 years is a long time for things to build nests, or perhaps some trash got jammed in there in 2011 and was never removed.

If you wanted to needlessly overcomplicate things and add more stuff to fail confusingly you could configure an additional check valve so that the condensate drained into the line but the sump discharge did not go into the condensate drain stack. That is not an approach I would suggest, but it COULD be done. 

To fix yourself, just replace the small pipe with a pipe that runs from the condensate tube to the sump (with an air gap so it cannot siphon) and close the valve, or cut and cap where the valve was. Possibly clear out the drain if it does not work with the valve closed (perhaps that's why you think you need a plumber now...?)