tl;dr: You might own the software that you purchase, depending on the seller's legal ability in court.

According to traditional product laws in the US, digital products would continue to follow more global considerations on the matter, but thanks to heavy lobbiyng [and the usual corruption associated with that here in the states] starting a few decades back, special exceptions to ownership/copyright laws were made in regards to treating digital products as services and further restricting consumer rights in regards to any digital product containing security measures [which was used to further solidify a company's rights to any product containing a DRM] under digital security laws.

While early ownership laws relating to physical copies [being treated as services] were rather dubious and mostly ignored by consumers, modern distribution platforms being considered as subscription services [rather than as product distribution platforms] has been a conception rather more difficult to dissuade against, due to the fact that it does in fact share many similarities with other subscription services. As service laws differ somewhat from product laws, it would make for a challenging legal battle.

Consider making microtransactions in a [free-to-play] MMO. The US requires that you receive what is advertised, but they do not require that you retain access to that content [rather understandably, considering the typical MMO's lifespan], nor do they prohibit your account from being banned if you violate terms of service [that again being a power that can be necessary for associated developers to have].

Purchasing a pay-per-view movie through a cable subscription is also an example of a purchase made through a subscription format, wherein you're not expected to retain ownership. More associable are gaming subscriptions like Origin Access, where you retain rights to available games so long as your subscription is considered active.

None of those examples directly compare to the Steam framework, but by lobbyists cherry-picking off the most favorable perceptions of such concepts, they've managed to hammer out quite the comfortable niche for digital distribution. [As per Archie's first paragraph, below.]

Most notably, Steam has made a distinction between access to their download servers and DRM, and access to purchased games. Thus, you'll always have access to anything you've downloaded, but Valve does not guarantee access to download or authentication servers. Banning an account would simply be an extension of removing access to such elements, and thus be something they'd feel comfortable having the right to do.

Even if it was possible to overturn current laws in the courts, it wouldn't be likely within the current legal environment and, due to the finance-driven legal system here in the states, it would be hard for most of those inclined to bring the matter to court to overcome the expenses involved with combating against a titan such as Valve.

Mind you, I'm personally entirely opposed to the current framework as it exists here, but it's important not to ignore how deeply entrenched the matter actually is. While many of Valve's legal arguments to Australia and the EU came across as absurd, they'd be fully accepted as valid here in the states, especially with how habituated the average citizen has become to Steam's form of PC gaming. Without a shift in how distribution platforms are perceived, they can continue operating under the umbrella of subscription services, and exploiting the benefits of such an association.

You do not rent/lease games from Steam. You buy from Steam a license to play the game on Steam platform, assigned to your account, with terms further defined in Steam ToS. That license is a digital product same as everyone else, and it's not a lease/rent contract. The license is perpetual.

The most important point in that article that many people are not aware of is the one stating that ToSes and EULAs are not laws, and this is something a lot of people do not realize. You can sue Valve on legal basis regardless of the situation and nobody can revoke that right from you, even if they state such paragraph in their ToS, at least in the EU (not making assumptions based on US since there is another level of anti-consumer practices going on there).

Provided you have enough of money to cover all the lawsuit costs, you can sue everybody and everything as much as you like, and as long as you can back up your claims through the actual law or strong enough arguments (such as Steam revoking access to your licenses for no reason), you're very likely to win. And you do not actually need to go to the US court regarding this, because Valve operates in EU with EU department in the Netherlands, and is subject to at least EU/Netherlands law.

This is the exact reason why Valve is changing how Steam works, as for example refunds are mainly related to the requirement of such guaranteed by the EU, and provided also to others (like US citizens) as "an extra", to not cause a shitstorm over EU citizens having more rights.

The only revocation of the license to the game that is permitted, is either:

• Payment failure, where you did not complete the transaction as you should, such as a chargeback. This terminates the license since you've never obtained it.
• Valve going bankrupt (unlikely and complex process)

This is why even completely banned Steam accounts can still log in and access the licenses tied to their accounts, even if all other Steam functionality is disabled, including any community interaction or buying further games. For example accounts that did a chargeback, which automatically terminates the account, end up in this state, even if logically Valve losses actual money in this (related to handling chargeback at least), and it's more than justified to terminate the account entirely for doing something like that.

Another view supporting the above is the situation where you obtained the license to play some game, while the actual IP licenses included in that game expired. This happened for example with GTA:SA music (and Mafia 1 too I think?). Steam was forced to make the game no longer available for new people due to that, but they were also forced to keep the product that people have previously bought, and they couldn't just "update" the game with cut-off music for everybody and act like nothing happened. This is why people that bought that game before the expired license, can still access the original game with original music, even if people that buy it today receive entirely different product. The logical and easy way would be to just update the game, cutting on the copyrighted music, but that could be a lawsuit case easily, even if it's irrational that one could sue devs for releasing a patch.

The most important point in that article that many people are not aware of is the one stating that ToSes and EULAs are not laws, and this is something a lot of people do not realize. You can sue Valve on legal basis regardless of the situation and nobody can revoke that right from you, even if they state such paragraph in their ToS, at least in the EU (not making assumptions based on US since there is another level of anti-consumer practices going on there).

So much this

Note that this makes Steam and Valve wholly liable for harm done to customers by all these idiot devs who are revoking keys for games bought in bundles.