The ADA covers usability and accessibility of publicly-accessible spaces (even those that are privately-owned) by people with disabilities, it's why wheelchair ramps and accessible parking spaces aren't optional.

Courts have historically not cared much if it's an established legal precedent "but on the internet" - just being online doesn't mean it's not covered by existing law (it might not be, but only if being online makes substantial enough difference). If someone with a disability like addiction can't use a publicly-accessible service (even if it's privately-owned) because the operators of that service aren't providing required accommodation for their disability, that could be argued quite convincingly to fall squarely under the ADA's authority.

It could also be argued that it's discriminatory to show known alcoholics booze ads, like a department store putting the wheelchair access ramp in the loading bay in the back of the building or blocking accessible parking spots with shopping carts.

For a practical example, if the customers at a grocery block all the accessible spots with carts, someone who needs one could sue the grocery for not keeping the spots clear. Their argument would be that while the grocery didn't put the carts there, they also failed to keep any accessible spots clear of obstruction as they are required to. Deliberately advertising booze to alcoholics would be like video evidence of the grocery employees putting the carts in the accessible spots, it could lead to hefty punitive damages or fines as well.

Edit: Please take note of the word "deliberately" above. For a sure cash judgement with punitive components, the plaintiffs would have to show that the advertising was based on data showing the person has a drinking problem; for a win that would just get things changed, the argument would be there should be toggles to manually disable certain classes of advertisement.