Well everyone knows that winning in lottery is something not so easy and it is a luck based chance that will only hit if you are extremely lucky. If we gamble on other games, the chances of winning are far more than as compared to the lottery. Not only that, the amount we need to participate in the lottery is very minimal so a lot of people will lose but they won't be feeling bad about it because they have not lost any big money.
You can participate in lotteries thinking that the little money you put in gambling will go in vain and wasted but if you are lucky, it can win you a jackpot. Its a game of luck and we never know when we may be lucky. Not participating in lotteries means that we are not giving that 0.01% chance of getting quick rich. Since it does take much to participate, many people are willing to try their luck. Just like that mom stories in the OP post, if she hadn't participated and given up, she would not have been the winner of 50,000$.
We're not anticipating thousands or millions of dollars worth of rewards when gambling on other games, which is why our chances are considerably better. Moreover, most gambling games have very specific outcomes (see roulette, dice, football betting, and so on), while the lottery is composed of numerous tickets with only a few actually winning anything of value. Add the low purchase cost and the large audience you mentioned, and your chances are statistically close to zero.
Personally, I'd rather use that money towards something else; these insignificant amounts we're discussing now can easily add up to reasonable amounts that could be used elsewhere.