Now, for electric cars to put them out of business, they'd have to be a relevant percentage of total vehicles - and overall, that will certainly take time. But the case becomes different in specialty markets. Different states and localities will (and already do) offer different EV incentives, and the natural use case for EVs varies between locations (urban/suburban/rural, mild vs. hot vs. cold climate, terrain, geography (isolated islands or areas without good road connects to the outside world, for example), areas with different driver profiles, and so forth). So an overall EV adoption rate of 1% might actually be 10%, 20% or more in certain areas. That could well be enough to start driving gas stations out of business in such areas, creating a potential contageon effect.
That said, business owners aren't stupid, and one expects them to adapt. For example, where appropriate one would expect gas stations to respond to increasing EV penetration by adding rapid charge stations. Electricity is cheap, but if someone needs a rapid charge (for a road trip or whatnot), they'll pay the going rate, even if it's similar to the cost of gasoline per unit distance traveled. They're not just going to say "meh, I'll just plug into a wall socket and wait overnight". So if you have an existing gas station with all of its capital costs of installing tanks and pumps already paid for, one would expect them to keep selling gasoline even as an increasing percentage of their customers switch over to electricity. Maybe they'll find it cheaper to remove broken pumps than fix them. Maybe they'll eventually hit a point where it's no longer cost effective to maintain their fuel tanks and have to stop selling gasoline altogether. But neither of these things are a "suddenly going out of business because EVs just showed up" scenario.
(Of course, there's a counter to what I just wrote, which is that - given that only a small percentage of EV charging will ever be fast charging - you're looking at a smaller potential market)