There isn't one answer to this, not least because HD sell it as "hardwood" so even the species isn't known. But even if the species were known (and it never changed1) wood can always be different from the textbook numbers because it's a natural material and it varies. Even pieces from the same tree can vary a lot or a little.
On top of that the flow of grain down the length of the dowel is critical to its strength2.
As if that weren't enough how well the dowel fits your drilled holes in the side 2x4s will have some effect on strength with many glues3.
So how much weight can this hold?
The only way to know for sure is to find out empirically — try it and see.
If this is for something important I'd make a sacrificial test piece, being just as careful with its construction as with the final one. Then test it to destruction by adding more and more weight until it fails. Then you have your answer.
Some assembly tips:
- Don't drill the holes freehand. If you don't own a drill press there are various jigs you can quickly make to help you drill square.
- If the fit of the dowel is not very tight I'd recommend using epoxy.
- Wax the centre portion of the dowel well during assembly.
- Be sure to sand the dowel lightly just prior to glue-up, here's why.
- Surprisingly given the title there's relevant info in this previous Question, Where should the trademark be placed on a baseball bat?
1 Which I would expect not to be the case, not across the entire country with all the various hardwood species that are locally abundant and cheap. For all we know it could be oak one place, maple another and something else elsewhere.
2 The more longitudinal the better. On the dowel pictured, see the chevrons facing the camera? Those are grain lines and they indicate the flow of grain in that particular piece is at an angle, something called grain runout. You want there to be minimal (less than in the picture) or no runout in the piece you select to maximise strength.
3 Commercial dowels are notorious for only nominally being the size they're sold as and you can fully expect these to be no different. Dowels can also shrink differentially, ending up with a slight oval cross-section. Plus, even assuming your drill bit is exactly to size that doesn't guarantee each hole you drill with it will be a uniform 1" diameter.