The link that DPH provided doesn't provide the entire picture here, so let me fill in what's missing. Texas imposes a sales tax on the sale of a "taxable item." Texas Tax Code (TC) section 151.051. The rate of tax is 6.25% of the sales price. Id. A "taxable item" means "tangible personal property and taxable services. Except as otherwise provided by this chapter, the sale or use of a taxable item in electronic form instead of on physical media does not alter the item's tax status." TC § 151.010. "Tangible personal property" means "personal property that can be seen, weighed, measured, felt, or touched or that is perceptible to the senses in any other manner, and, for the purposes of this chapter, the term includes a computer program and a telephone prepaid calling card." TC § 151.009.
Therefore, putting all those provisions together, a DVD of a movie that you buy at the a store in Texas is subject to the Texas sales tax because a DVD is tangible personal property (i.e. it can be seen, touched, felt, etc). If you downloaded the same movie over the internet from a Texas retailer, that too is subject to sales tax even though it cannot be "seen, weighed, measured, felt or touched" because the Texas statute says that sales of an item in digital form rather than on physical media (the DVD) does not alter its tax status, making it taxable just like the physical product. Similarly, a computer program constitutes tangible personal property no matter the form in which you buy it (i.e. whether you buy it on a CD-Rom or download it). So, Texas sellers must collect sales tax on those digital products that you buy from them.
So, why don't out-of-state sellers that sell to Texas residents have to collect the sales tax? The reason is that the U.S. Supreme Court held that under the federal Constitution the states lack the power to compel an out-of-state seller to collect sales tax unless it has a physical presence in the state. Quill Corp. v. North Dakota, 504 U.S. 298 (1992). The court said that Congress could change that rule by legislation, but so far the Congress has declined to do that. The rule from the Quill case is why the company mentioned to you that it was forced to collect the tax in Texas—Texas evidently found the seller had some kind of physical presence in the state, which then allows the state to compel the seller to collect the sales tax.
But that's not the end of it. Every state that has a sales tax also has what is called a use tax. In Texas, you'll find the use tax imposed in TC § 151.101. Part of the purpose of the use tax is to prevent residents from avoiding the sales tax by buying taxable goods from out-of-state sellers who don't collect the sales tax. That's important for two reasons. First, it helps preserve the state's revenue. And second, it helps to ensure that residents don't end up sending business out of state just to avoid the sales tax. The use tax is imposed directly on the buyer. It is imposed on the the purchase of the same goods and services as the sales tax, and at the same rate. Thus, when you buy a taxable item from some out-of-state mail order seller that doesn't collect sales tax on it, you are supposed to file a use tax return and pay the use tax on the item. Most individuals are not even aware that their state has a use tax, and states have had trouble enforcing the use tax because they lack information on the out-of-state purchases of their residents. In this computer age, however, states are increasingly able to get that information and enforcement is improving. The link that DPH provided discusses briefly the use tax.
So, while you probably didn't know it, you were required to pay a use tax on the digital content/software that you've been buying from vendors who haven't collected the sales & use tax on the sale. Therefore, whether the vendor collects the tax for the state or whether you pay it as a use tax, you are liable to pay it either way.