Obviously I'm late to this question by a few years (yikes), but I'll take a swing anyway.
In modern Games, the Producer is usually in charge of getting a part of a game done. Many years ago, when game teams numbered in the low 10s of people, they might have handled the entire game. Nowadays, across a lot of the industry this will probably be one vertical or horizontal slice of a game. Some examples of how it might be organized: Multi-player, Tools, UI, Character art, or level design. Depending on the company, they might have creative input (and there may be a complimentary Development Director role), or be more focused on schedule and budget. The pithy answer is: they move the ball forward.
If it's a place that allows creative input, they also maintain the creative direction for their defined area.
The EP in games is pretty different than its counterpart in film. The role is usually in charge of a franchise (he/she might manage game development as well, as a 'project lead'). They help define the creative direction and then ensure it is followed. They define and manage the budget for the production. They approve changes to either, and (they should) take the hit when those changes are wrong. They give direction to the creative and engineering leads, and most cases, those people report to them - at least as far as their work on the franchise is concerned. Because we're talking about a franchise, they also direct decisions about patches, expansions and live support. They're involved in marketing and in some cases, sales decisions.
I've never dealt with this role, but I'm going to say it's probably analogous to Project Lead.