I'm no expert, but I'll give this a whirl:
Lets go through your requirements one by one and what components you need to for them.
Android Development: In all honesty, I don't think you're going to be hardware limited here, anything should be fine.
Mid-Level Gaming: Let me ask you what type of display are you going to be using. Because in all honesty, an R9 380 is more than enough to play games at 1080p at almost maxed out settings. If you have a higher resolution or framerate display, and you want to play with all settings maxed out, then perhaps I would recommend a R9 390/970 (though would pick the 390 simply due to better DX 12 compatibility and 8gigs of ram vs 3.5 in the 970).
But in all honesty I think a 380 is going to be more than enough for your needs (assuming you're defining mid-level gaming the same as I am). Keep in mind, your system in its current state won't be VR ready. If you want VR, then I would recommend a higher end graphics card. Anyway...
Video Editing: This is somewhat complicated, because I don't know what editor you're going to be using, what codec/format you're going to be working in, and your general work flow. But here's some general advice.
Video editing is by and large CPU limited, so you want the most powerful CPU you can get your hands on here. Definitely an i7...and possibly if you're feeling adventurous get a Xeon processor simply because it has more cores which will massively help in scrubbing and rendering videos.
Maybe in order to save some cost, you may want to experiment with using a non-skylake CPU, such as an i7 5830 or something that has more cores and threads than the currently available i7 6700. Again for rendering, you want more cores, so thats why I would recommend that. Also if you're using a last generation cpu, you can use a cheaper x99 chipset/motherboard as well as the cheaper DDR3 RAM. Just something to consider.
I'm not an expert, so don't quote me, but for most video rendering processes, you're CPU limited and very little of the processing load is shifted off to the GPU. IF you're sure that your workflow utilizes the GPU, then of course, I would recommend at least an R9 390. But just check over your workflow before committing to a more expensive gpu.
Graphics Editing: Again this is CPU limited, so as long as you have a powerful CPU capable of video editing, you should be ok here.
Here's a possible setup with the prices taken from czone (neither recommend or discredit this retailer, just easier to grab prices from here):
CPU: i7 6700 (not the k version, don't know if you're into overclocking) ~ 35k
Chipset: Gigabyte H170 ~ 12k
CPU Cooling: Coolermaster Hyper 103 (honestly I would prefer a better fan cooler, but czone doesn't have one avaible.) 3k
Memory: Corsair Vengence 32 (you can use 16, but the more memory will help you in development and editing): 24k
Hard Drive: 2 Seagate 3 TB Harddrives (you need a lot of storage space for uncompressed video) at 10.5k each: 21k
SSD: Kingston 240 GB drive: 8k
GPU: Gigabyte R9 380 w/4 Gigs of RAM: 28k
Power Supply: Thermaltake 600W gold PS: 10k
Total: 141k
Case: Anyone of your choice, just make sure it fits everything, but you have 9k left over
A couple places to save money: I feel the RAM is very expensive, if you can get some from overseas, I would recommend that. Eg you can get 32 gigs fo GSkill Ripjaws for about 18k. And usually I've rounded up on prices a little bit also; I'm sure if you shop around you should be able to buy those components and maybe even end up saving up to 10k from this budget.
Also checkout your harddrive needs, you can probably take it from your old computer as well.
Another note, is that I didn't choose the 6700k cpu for you, if you're going to overclock it, you need to watercool it so that's going to increase your cost by another 20k.
Please note this includes ZERO peripherals as well as no display, and I've eaten up your entire budget. We need to change things quite a bit if you want to include that in this budget as well.
Just as another piece of advice, I would recommend you setting aside another 10k (either additionally or save money in your compoenets somewhere) as random expenses tend to pop up.
Hope this has been helfpul, good luck.
