I'm wondering if a larger blockchain means that running a full node is computationally harder, i.e. requires more resources?
(maybe more verifications should be done?)
Yes, it does.
The first obvious requirement is a larger storage space needed for the raw blockchain.
The second one is the need to store an increasing amount of output data in fast storage, as they're randomly referenced by incoming transactions. This include key images, public keys, and amount masks. This set never shrinks.
If you also consider that the amount of transactions per unit of time increases, then you also need more CPU, memory, and network capacity. This is not implied by your question though.
There is no pruning in Monero currently, but this is something that is doable, and preliminary work was done to hash prunable and unprunable RingCT parts separately. There is also talk of dropping signatures beyond a certain age (ie, when they have more than a huge number of "confirmations"). What will be done is not yet decided though.