Why do you think intervention in Syria would lead to WWIII?
The purpose for regime change in Syria is to make it easier for regime change in Iran.
Iran is also the reason we changed the regimes in Egypt, Turkey, (and any other country that we just did regime change in over there that I haven't paid attention to), etc..
[side note- Turkey is a little more murky(oh shit that rhymed) as our agents sided with the opposite radical group than usual. That may have been just been a sign of how skilled we now are at regime change, that the specific pawns are meaningless(my guess as most probable) or it could have been a proxy war of sorts on the regime-change level(something which we need to expect as an eventual reality, but I doubt we have real competition). ]
So Iran is the objective and Syria is a stepping stone.
The regime change has been planned for a relatively long time, as has been catching Syria and the brutal Assad in the act of using WMDs if Syria (supported by Russia and the East) withstood the media and the terrorist agents destabilization efforts.
The WWIII part comes in because it is not clear whether the system can withstand the Western Powers aggressively changing all these regimes and changing Iran's regime.
Iran (and Syria (and the other regimes we've been changing) represent somewhat of a 'balance' of powers for the Eastern Powers. Iran is a nuclear power in the middle east for the Eastern Powers.
Syria is a Russian proxy state with a mid-level military, and a Russian naval port.
When the West takes these for themselves, Russia loses all those investments, and the Eastern Powers lose a significant amount of military leverage.
If the Eastern Powers can't withstand that aggression, they may HEAVILY support Iran (or even Syria). They may also pre-emptively strike (most probable would be striking Israel by way of Iran).
The end game is very hard to see.
The mass media for all sides never talks about the end game (and what they do talk about is fictional stories about the current goings ons that tend to confuse most everyday people), so the best you can do is look at the system and make guesses like I just tried to do.