It's not really fair to speak of Vimeo "caving".
The way the DMCA is set up, service providers like Vimeo are protected from liability if they promptly remove/disable access to material when they receive a DMCA request. It's not their place to assess the merits of each claim. In fact, doing so would be dangerous. If they said "This claim is obviously bullshit," and left something up, and a lawyer was able to prove later that it wasn't, they would face heavy penalties. No business can function like that.
When I worked for a similar video hosting business, our policy on receipt of a DMCA was to (a) take down the material as required by the law, (b) immediately notify the poster and point them to useful resources such as Chilling Effects, and (c) explain to them how they could send us a counter-notice, which we would then pass on to the entity claiming copyright. If the claimed copyright holder didn't then notify us that they were bringing a lawsuit against the user within the period allowed by the law, we would promptly re-enable the content. We made a point of expediting every part of the process as much as we could, in order to get legitimate content back online quickly as possible.
This is what the DMCA requires, and this is apparently what Vimeo is doing. It's not actually that bad a system in some respects. Where it falls down is that there's no penalty for abuse of the system by entities like Entura or other bad actors. There's essentially no cost to sloppy or malicious filing of DMCA reports, so 'anti-piracy groups' feel free to fire off takedowns in scattergun fashion.
Even if there were just a "Three strikes and you're out" rule for bogus DMCA notices, outfits like Entura would have to be a lot more careful. I would love to have been the one to send back a message saying "Owing to a large number of bogus DMCA claims originating from your business, processing of DMCA reports filed by you is suspended until further notice. Have a nice day."