Solved and thus claimed. It would appear that the only thing I lacked doing was adding 10 and selecting a decoding sequence A-Z0-9. My method had therefore been correct all along, but assumed incorrect due to the code's composition. One thing I didn't expect was a valid Steam key containing so few digits (it had one).
The solution for the uninitiated is to use the screen / video / graphics display resolution given on the right side of tilde as a product (height times width), divide by 10, subtract the number on the left side of tilde and finally add 10.
A reference for graphics display resolutions can be found here:
http://en.wikipedia.org/wiki/Graphics_display_resolution Set 1: 1280 x 768 / 10 - 98300 + 10 =
14 640 x 480 / 10 - 30700 + 10 =
30 1280 x 1024 / 10 - 131071 + 10 =
11 800 x 600 / 10 - 48000 + 10 =
10 1360 x 768 / 10 - 104434 =
24 This one is simply inputting the numbers.
Set 2: 1024 x 600 / 10 - 61445 + 10 =
5 1280 x 720 / 10 - 92166 + 10 =
4 1600 x 1200 / 10 - 192005 + 10 =
5 1920 x 1080 / 10 - 207356 + 10 =
14 2560 x 1440 / 10 - 368633 + 10 =
17 For this, each named resolution is looked up at the link above, and in cases where there were multiple possibilities the one yielding the lowest difference from the left hand side number times 10 is chosen.
Set 3: (WUXGA) ------->
1920 x 1200 / 10 - 230408 + 10 =
2 (WQSXGA) ----->
2560 x 1600 / 10 - 409606 + 10 =
4 (WXGA) --------->
1280 x 800 / 10 - 102385 + 10 =
25 (WSXGA+) ----->
1680 x 1050 / 10 - 176403 + 10 =
7 (WXGA+) ------->
1440 x 900 / 10 - 129604 + 10 =
6 For each of the same approach as above is used, however instead of a direct lookup, the possibilities need to be assessed. In the tables in the link above a number of large resolution with aspect ratio 16:10 needs to be computed and compared. The most likely candidates are chosen.
Thus the sequence of numbers is:
14, 30, 11, 10, 24, 5, 4, 5, 14, 17, 2, 4, 25, 7, 6.
The substitution is performed by considering 1-26 letters A to Z and 27-36 numbers 0-9.
I had figured that the other way around be more likely, but no.
The prize finally revealed to the public:
Vegas - Make It Big.
Thanks for the puzzle (and the game), Momo. ;-)