You are correct that the law (through the discretion exercised by prosecutors and the intent of Congress) has drawn a distinction between the activities of bookmakers and casual bettors.
This is interesting insight though. It goes in line with the argument that I was trying to make in my paper. It discussed the various ways prosecutors have tried to approach online gambling and how their efforts have had no deterrent effect what so ever. There was a recent move by the feds where they seized the accounts of 27,000 online poker players with over $100 million combined in them. It's the first time the feds have ever gone after individual bettors before. I argued that it's hard to send a message to bettors with moves this like because people who bet online (by and large) think that they are not doing anything against the law. (I mentioned that this perception was only going to be amplified by the fact that prosecutors were going after them using money laundering laws even though those laws require that you are trying to conceal the origin of funds gained through illegal activity. They still haven't mentioned what original statute was being violated to generate the illegal activity.)
I was quoting the Wire Act, but it's not solely applicable to wagers made over telephone lines. Any activity conducted over the Internet constitutes a wire transmission and courts have ruled that the Wire Act applies to online sports gambling. There's a case with BetOnSports with that holding.