As for voting being gamed by people - that is just a potential, just as people could potentially game the voting system for the polls and decide which party becomes government of this nation, but that isn't enough of a reason to not have a voting system in the first place. What we have to look at is, how likely is it to be gamed? for a political party to get in power - there is a huge amount at stake, but for a commenter to go to the efforts of creating multiple accounts to add a few votes to his comment popularity, and for what gain? a bit of obscure internet fame? Hardly that even, with the large numbers of people visiting the BBC site, many would bury and downvote junk comments into oblivion before they'd even have a chance of showing popularity. (Again, see working examples on social media sites like those I referenced)
These measures will increase interactivity and encourage greater participation - If I received an email alerting me to a reply, I would feel obliged to respond. If there was a profile 'control panel' that displayed how many people liked and disliked my comments, it would show that what I had to say was being noticed, and if it was appreciated by readers it would give the incentive to continue posting. This is social currency, but we don't have any of that to give and receive so we don't have the building blocks to let a social economy flourish on the BBC.
This kind of thinking assumes that the governing bodies of countries and the millions of citizens which populate those nations are one unit and body, when the reality is that for many populations, the people and its leaders are at odds, corruption in authority is strife and the leaders are more interested in power than the well-being of their citizens. For many of those people, they have gone from a state of poverty to worse. The government of Pakistan is not in need of your donations to survive, but the people of Pakistan are certainly facing huge difficulties and need every help they can get. Many people and nations don't like the leaders of N. Korea, but that doesn't blind us to the plight and poverty of its people. Similarly, we should not become hard hearted to a humanitarian cause because of our political biases and God forbid you find yourself in a similar disaster and see no help forth coming from your own governments, lest you have to eat the sourness of your own words.