Really interesting question! I'll give my two cents but take it with a grain of salt: I'm not much of an MMO player. I played GW1 for about a year, but have since only played FPS, RPG, RTS and other general action games. My perspective may be a bit off then.
Depth in combat isn't simply how many if-and-or-else effects a particular skill has as you mentioned above. Cross-profession combos and the compounding effects of various skills together adds some depth, but on its own isn't enough to draw my attention either. For me, it's about the variety of things one can accomplish in combat through use of skills, tactics, environment, and cooperation with other players. That's a little head-in-the-clouds kind of definition, but I'll try to break it down:
The variety of skills, what they can do, and how you use them in specific instances is the most obvious route towards combat depth. The more skills, the more complicated right? But complexity in itself doesn't mean combat has depth, it just means it's more tangled in formulas and harder to unravel, meaning most players will stick to the easiest uses while few will experience the true breadth of the skills available. Instead, having the right skills at the right time and knowing how to make the most of them is what adds the depth.
By tactics I mean the use of resources on the battlefield to ensure victory. Resources could be personnel in your immediate area, or traps laid by enemy forces, etc. How individuals or groups of people choose to engage the enemy (from range, in melee, pushing them away or funneling them to a kill zone) adds great depth to the feel of combat and gives a targeted goal to the player aside from dealing damage and staying alive.
The diversity of environments really makes combat a lot more interesting if it affects how players use skills and tactics. If everyone fought on a flat, open battlefield, it would be quite boring right? Instead, players have to pay attention to who has elevation over another, whether the easiest route to a keep is also the deadliest, or if there's a squad of enemies sitting around a corner waiting to ambush you. Aside from the physical implications of environment, there's the slightly more gimmicky aspects too (love them or hate them). The trebuchet in Khylo, the Quaggan in WvW, or the three dimensions in underwater combat are all aspects of the environment and contribute to what tasks or goals players set for themselves.
The last aspect is related to tactics, but the ability to work with companions to take down a target in and of itself directly contributes to the depth and engagement of combat. The cross-profession combos aside, if two players with different skills and tactics can coordinate to distract, harass, and defeat an enemy together, that just feels a hell of a lot more rewarding than standing alone in a field pressing 1-1-1-2-1-3-1-2-1-1-1 all the time.
I tried to keep those explanations brief-ish but I hope that adds to discussion