The HP would be better for gaming, but the Asus would be better for compiling code, though it would likely be abysmal in DOTA.
If you're willing to spend some extra cash, take a look at some of MSI's gaming series or Asus's ROG series notebooks. They have Intel processors which will work great for compiling scripts, and they also have dedicated GPUs that will give you great performance in games compared to either of the options you're currently looking at. However, they can be pretty heavy; my Asus gaming laptop weighs roughly eight pounds, but do note that mine is an older model, and they've gotten a lot smaller and lighter since I bought mine.
Most likely. Sadly, you'll be hard pressed to find an Intel-based laptop with any sort of acceptable graphics horsepower for under $800, and even that's pushing it, as Intel laptops require a dedicated GPU to be useable for most games. Intel's integrated graphics are terrible for anything more intense than typical desktop use. AMD on the other hand has made gaming-level graphics more accessible, especially on portable devices, thanks to their A-series APU chips, which feature both traditional CPU cores and mid-range GPU cores together on the same die. This makes AMD the clear winner for portable gaming on a budget.
However, there are a few important things to understand before you buy. For starters, while the HP will be better for gaming by comparison to that Asus laptop, it's still not going to be an optimal experience at all. On more demanding modern games, you'll be lucky to hit more than 20 FPS, and don't even try anything along the lines of Crysis 3 or Far Cry 4. But games like Minecraft, Fallout, or Skyrim should run fine at decent or even high settings as long as you aren't loading up hi-res texture packs or anything. Second is that because it's an AMD chip you may suffer from some minor to somewhat moderate performance issues in CPU-intensive tasks compared to if you were running an Intel CPU. Such tasks include (but are not limited to) video editing, 3D rendering, or, most importantly for you as a programmer, compiling. Lastly, heat output is going to be something to keep an eye on, especially when gaming or during heavy CPU loads. Consider investing a little extra money if you can on a laptop cooler for use when using your laptop at home. This one is the one I'd recommend the most heavily, as it's the most effective laptop cooler I've had experience with.