I checked the citations for that part of the article and they do not back up that claim. They are talking about what territory the USSR will get and which surrendering troops will become Soviet POWs. There is no discussion of "well, we better hold off because the 'mericans are just gonna glass 'em all for us".
Furthermore, the Americans had a shovel ready invasion plan with a start date in November. The soviets didn't have a real plan yet. It's not like they called off an invasion because we started lobbing nukes.
Anyone who says that showing the USSR what we were capable of was more than just a side benefit understand the Pacific campaign. If we didn't nuke them we were going to firebomb them. It was basically common knowledge that these people were dedicated enough to follow their cause to the death. What was learned on Iwo Jima and confirmed on Okinawa was that they were going to make us fight for every inch. In lieu of that it's hard to justify not using every available means to kill them dead enough that they surrender without invasion or soften them up prior to invasion. Imagine the scandal has Truman just decided "this whole atom bomb thing is barbaric, we're going to invade them and/or let the soviets burn half a million lives invading them".
It's hard to prove exactly, but Stalin's entrance into the war is almost certainly the precipitator for it's quick end without an invasion. For the Japanese, partial occupation by Red Army troops was a much worse prospect than occupation by American troops. For the U.S., giving Stalin a say in Japan was utterly unnecessary and very much undesirable at that point (as opposed to much earlier in the war). The A-bombs wouldn't have moved the Japanese military or emperor very much: they weren't more devastating that fire bombing already had been, and there weren't any notable cities left to devastate in Japan.