There are techniques and movement within Aikido that will work against boxers and wrestlers. But the common training approach won't make them useful in that context. To have a chance that an aiki opportunity will present with a boxer, I first need to be able to keep him from clobbering me or jabbing me to death. I need the ability to control the situation with movement, strikes, and/or grappling. A similar issue exists for dealing with a wrestler - I need the ability to keep him from taking me down before I can do anything. Once I can remain in the fight, so to speak, then there are opportunities to use what Aikido contains. I'll add that if you don't insist on an absolutely aiki approach (meaning, you train the techniques being willing to use muscle and leverage when they will work), then Aikido does have useful tools for grappling. If nothing else, practicing the techniques that way would provide a good foundation for learning to resist grappling (so better defense against that wrestler).I have some difficulty accepting that Aikido doesn't have an answer to boxers and wrestlers. Perhaps some of the Aikido practitioners will correct me if I am wrong. At least within the Aikido rule set. MMA has a different rule set, just as boxing and wrestling, and rightly so. Then one must consider the relative abilities of any two contestants.
Like @now disabled I have a curiosity about the way the Aikidoist reacted to the attacks. It may he was befuddled by a new rule set, I don't know. But he looked way more unsure of himself than I would have expected of someone who is allowed to have his own Aikido school.
I think the issue is that folks want to step in and use their Aikido right off, like they do in training. They want that first jab to end up with the boxer on his butt. Not likely to happen, unless he's being really cocky.