Working in the VFX side of the industry, if you're talking about real-time viewport previews and not production rendering, then Maya and 3DS Max typically also use OpenGL (or possibly DirectX -- pretty much the same).
One of the main conceptual differences between VFX animation software and games is the level of assumptions they can make. For example, in VFX software, it's not uncommon for the artist to load a single, seamless character mesh that spans hundreds of thousands to millions of polygons. Games tend to optimize most for a large scene consisting of a boatload of simple, optimized meshes (thousands of triangles each).
Production Rendering and Path Tracing
VFX software also places the emphasis not on the real-time preview but on production rendering where light rays are actually simulated one at a time. The real-time preview often is just that, a "preview" of the higher-quality production result.
Games are doing a beautiful job of approximating a lot of those effects lately like real-time depth of field, soft shadows, diffuse reflections, etc., but they're in the heavy-duty approximation category (ex: blurry cube maps for diffuse reflections instead of actually simulating light rays).
Coming back to this subject, the content assumptions between a VFX software and game wildly differ. A VFX software's main focus is to allow any possible kind of content to be created (at least that's the ideal, although in practically it's often nowhere close). Games focus on content with a lot more heavier assumptions (all models should be in the range of thousands of triangles, normal maps should be applied to fake details, we shouldn't actually have 13 billion particles, characters aren't actually animated by muscle rigs and tension maps, etc).
Due to those assumptions, game engines can often more easily apply acceleration techniques like frustum culling which enable them to maintain a high, interactive frame rate. They can make assumptions that some content is going to be static, baked down in advance. VFX software can't easily make those kinds of assumptions given the much higher degree of flexibility in content creation.
Games Do it Better
This might be kind of a controversial view, but the game industry is a much more lucrative industry than VFX software. Their budgets for a single game can span in the hundreds of millions of dollars, and they can afford to keep releasing next-generation engines every few years. Their R&D efforts are amazing, and there are hundreds upon hundreds of game titles being released all the time.
VFX and CAD software, on the other hand, is nowhere near as lucrative. R&D is often outsourced by researchers working in academic settings, with a lot of the industry often implementing techniques published many years before as though it's something new. So VFX software, even coming from companies as large as AutoDesk, often isn't quite as "state-of-the-art" as the latest AAA game engines.
They also tend to have a much longer legacy. Maya is a 17-year old product, for example. It's been refurbished a lot, but its core architecture is still the same. This might be analogous to trying to take Quake 2 and keep updating and updating it all the way up until 2015. The efforts can be great but probably won't match Unreal Engine 4.
So anyway, that's a little take on that side of the topic. I couldn't make out whether you were talking about real-time previews in viewports or production rendering, so I tried to cover a bit of both.