On the original question I would say that it's hard to know whether the crew did the right thing in this particular case because we don't have enough information.
In my mind I'm wondering what made the crew assume that there was a comms equipment failure just because they did not receive a response? Were other aircraft in good communication with the TWR controller? Did the crew try to check that they could communicate with other stations on the freqency? Did they try a second box? Did they #7600 to indicate to the TWR that they would follow the RCF procedures (I don't know if LEMD TWR would see it but it's possible)? Did they look for light signals from the TWR (quaint I know but sometimes still happens)? Did they try and call GND when they assumed that comms with TWR were U/S? Did they keep calling for clearance or was it a once only request that didn't get an answer?
If there was no RCF but TWR simply couldn't reply at that moment for some reason, then I would suggest the crew actions were probably not correct. In normal operations the whole ATC system is based on permissive instructions, that is to say that you can do something is ATC says you can do it - the absence of permission means that you can't. It's built that way to be more robust and to fail-safe in most situations. If you take this proposition to its logical conclusion then you might as well do away with ATC because crews will do whatever they want if they don't hear the permission when they want it.
Just because the runway looks clear of traffic doesn't mean it is or it will continue to be. Landing when the runway looks clear but without the appropriate clearance involves/introduces risk into the operation. In a non-normal situation this increased risk may be deemed acceptable or preferable to the available alternatives...but not in normal ops.
So I would suggest that whether this was a good decision or not revolves around the reasons that RCF was assumed and we don't have enough information. Of course the crew had something in the order of a minute and a half to do all of the assessment, double-checking and decision making...and still had to fly the aircraft. In practice, landing is quite probably a reasonable action but I can equally see arguments against.
Maybe one possible alternative in the circumstances described - and I don't know whether it is feasible at LEMD - would be a go-around into a visual circuit. This will certainly get ATC's attention and will soon have them trying to call the aircraft which will help to establish whether there really is a comms failure, it gives a bit more time to assess the situation, try another box, maybe to call another agency and see if comms be established through another channel, maybe even see some light signals (OK, I know that one's a bit of a long shot) etc.
Just a few thoughts from the ATC perspective.