I believe the answer is "it's neither a product or a service, it's a scam". It's basically EA trying to gouge gamers to spend more money on an already expensive product. For all comments about the costs of running servers and the like, game companies have been providing these things as part of the product for a very long time, and the inclusion of things like those servers is part of how they were justifying the high price tag to begin with. When your looking at a multi-billion dollar industry it's hard to really have sympathy for stuff like this.
I'm not really sure that gamers are quick to embrace/support this either. I think the issue is mostly that we're not given much of a choice, and so far the gaming populance is a big enough group of addicts where we have not actually refused to patronize the gaming industry as a result. That may or may not be coming for more people due to the fact that I have probably seen more anti-industry sentiment recently than ever before.
I will also say that while piracy is wrong, to fight it takes consumer support. You'll notice that in pretty much every discussion on piracy you wind up with tons of people that defend it. That defense comes specifically because of practices like the ones being discussed here, "is it a product or a service?" and "you need an internet connection" and "$10 for multiplayer access that used to be part of the product".
This is why I say with some frequency that the whole "piracy" issue is basically two criminal gangs going at it. Neither side can claim the moral high ground. The game industry is both greedy and engages in corrupt cartel-type behavior like price fixing. The same kinds of stuff that has the federal goverment constantly at the throat of the gas stations/oil companies. Then you've got the pirates who are outright thieves, however in their case it's careful not to make a "Robin Hood" type analogy because for all claims about the safety of piracy I think these "botnets" and stuff come from these guys using "warez" to infect people's systems, which in many cases is probably their motivation to begin with. Not in every case of course.
I think Steam gets the support it does largely when there is no other option, or they are running a major sale on a product. I, and others, feel that paying full retail price for a game you have no direct control over is ridiculous. I mean consider that some people like me still play games like "Arcanum", or the original Fallout games. Buy your game from Steam and you want to play it in 5 to 10 years you might be totally out of luck, for all we know they could go out of business... hey, people thought companies like "Origin Systems" (once a titan, Richard Garriot could afford private space flights for a reason) were unstoppable titans, but then they got bought out and disappeared.
What's more, since The Internet costs money (and is becoming increasingly expensive as companies find ways to charge more and more money, and the basic service requirements to function online increase) I'm wary about the entire idea of internet connection being required to activate a game, never mind play it, or obtain all of the initial content your entitled to when you lay down your cash.
Truthfully I think what we need is consumer advocacy, though getting enough gamers to organize for something like that would be very difficult. Then we need to see that advocacy challenge the industry on even terms and fight to get things defined fairly along the service/product lines, ensure consumer protection of what they are paying for, and similar things.