Amadeus and Sabre systems are probably the biggest single point of failure in the world. I cannot find any other service which, when made unavailable, will cause workdwide chaos.
It seems that there has been a networking issue, rather than software issue. So blaming code(rs) here is like blaming manufacturers of TV that doesn't work for you because you have no electricity.
It's not the cloud per se. It Amadeus, like its rival SABRE, is mostly mainframe based systems (though it has been moving away from that for the past 20+ years). These systems were built in the 1960's. They are actually very reliable but when they go down, they take all their contracted airlines with them. There are only a handful of these companies and those two are the main ones.
It's a c++ application running against a set of Oracle databases. These are the systems which replaced the older mainframe ones handling check in etc. Some comms with certain mainframe systems managing inventory for some airlines is possible, but less likely for these airlines running altea.
Why is that a problem? If you're Heathrow you care about how much overall downtime you have, you don't care about whether you're down at the same time as Charles de Gaulle. If anything having downtime at the same time as everyone else is probably less of a PR issue than having downtime while all the other airports are doing fine.
With cloud I meant the airlines which don't have their instance installed on-premise (or at least in a different data center). If each airline had their own installation, a failure would bring down the data exchange with that airline but not the operations of all airlines.