Deity is a very different animal than the lower difficulties when it comes to ICS. Some considerations:
1. AIs with more cash.
2. AIs that REX like mad.
3. You have to play tech catchup early on. Need a military tech advantage to win war, unless you have a broken unique unit. So war for land is not a solid early option.
The game constraints definitely steer you towards REXing, because you need luxuries to sell for Research Agreements, which allows you to keep up on tech. You can't get the luxuries from early war because it's simply not feasible most of the time, or has a huge opportunity cost. The AIs are expanding like mad, so if you don't settle quickly, you'll lose out on some luxuries and city-locations.
You're forced to ICS like mad and turtle until you come upon a military tech advantage. This times nicely to the end of your happiness consolidation phase, allowing your excess happiness to be turned into more cities (or more citizens in your current cities).
Emperor difficulty and lower, it's not too hard to grab a military tech advantage much earlier, there is considerably less pressure for Research Agreements, etc. which frees up the ability to play differently (ex: less cities + puppets) and still keep up or get ahead in tech.
This is my issue with Civ5 at the moment - Deity play is extremely homogeneous, but any difficulty below is not challenging enough. I think I'll stop playing Continents, because the impetus for Astronomy for overseas RAs/luxury sales is such a limiting factor on other strategies.