I think the question of whether Twitter is a "media" company or a "technology" company is ill-conceived.
The better dividing line is that there are some companies whose primary business is selling a product to customers, and other companies whose primary business is selling an audience to advertisers. It's also quite possible to be in both businesses. Google, for example, is primarily a company that attracts users to its Search, Mail, Maps, and Docs services and then sells an audience to advertisers. But it also does have a business where it sells ad-free versions of its online services to enterprise customers.
So whether you call it media or call it tech, Twitter seems to clearly intend to move in the direction of becoming an advertising business.
It seems like a mistake to me, if only because as it currently exists my twitter feed is already full of what amount to ads. A lot of the culprits are people just like me—journalists touting our latest articles. Then you have various other media personalities, celebrities, and authors investing in their personal brand. You have food trucks telling you about their location and local restaurants touting specials and deals. Every big company has one or more corporate twitter accounts these days for PR and marketing purposes. Rather than selling lots of ads on Twitter, Twitter could sell itself as a service to the large number of people and firms who are already organically using it as an advertising tool.
Which is just to say that the Twitter user base seems ideal for a tiered pricing model. Most people on Twitter don't tweet that much, don't have very many followers, and don't particularly aspire to having a large number of followers. Then you have a relatively small minority of heavy users who are deliberately courting a mass Twitter audience. Just charge us! Let everyone with fewer than 500 followers use it for free, and then have a few tiers of pricing for people with large followings. Most people probably have no desire to pay for Twitter, but anyone who's bothered to amass 20,000 is obviously getting a lot of value from access to the Twitter audience and would pay for it. Meanwhile the broad mass of non-professional users could keep using a great no-charge ad-free service that creates the ecosystem pro users want to pay to gain access to.