The approach would be the same to all companies - identify the revenue growth. break down where the revenue comes from, who's the customers, # units, sales price, etc. So with TiVo, same thing - how many customers, average price, growth rates, etc. Then, break down the costs that TiVo has. A retail business like TiVo (consumer oriented in particular) is always easier to approach in an interview (or on the job) since chances are, you've heard of them or even use the product. It's really no different than asking how many Gillette razor blades would be sold, etc.
Even though you may never have used the product (TiVo in this case), the approach wouldn't actually vary too much. So since you indicated that your cable box does the same thing, then that is a detriment to TiVo and would limit TiVo's growth. So, one could take the market share approach and figure out % of TV watches that use cable and DVR-functions, etc.
Partly, this comes from experience and realizing that all companies essentially are approached the same way. Take our segment build-up class which goes into 4 different ways of analyzing 4 different businesses.http://www.wstselfstudy.com/package3.html