Pruning the Monero blockchain, a number question

Why only 2/3 of the blockchain data can be pruned?

Think about it like this: If you pruned 100% you would have nothing, your node, and wallet connected to your node, wouldn't be able to do anything. So how much do we actually need to keep to still be usable? Well, once we've verified every transaction, we no longer need the signatures, so they can be discarded. However, we still need the rest of the tx data.

Now to be usable to others...

How do I relate 7/8 (87.5%) pruneable transactions to 2/3 (66.6%) pruneable blockchain?

With pruned nodes, we still want them to be useful to others also, so they can sync and crucially verify every transaction. This is where the 7/8 comes into play. Of a full blockchain, we will only prune 7/8 of it, leaving a random 1/8 unpruned, so others can still fully verify that 1/8. When a new node comes along, it will sync and verify parts of the blockchain from many different nodes.

So, 7/8 will be a candidate for pruning and of this 7/8, ~2/3 can be discarded.

Or to put another way, 1/8 will be left untouched, of the remainder, ~2/3 can be thrown away after we have verified.

The 2/3 number in the linked article is speaking approximately* as to how much will be discarded from a full blockchain - bottom line is this, 1/8 will be kept unpruned (untouched), the rest can be pruned, which means discarding parts of data we no longer need (e.g. the signatures), post verifying.

*approximately because transaction size and volume are not uniform.

Which component of the transaction is actually pruned?

Signatures.

This pruning is not as efficient as bitcoin

Comparing is pointless. The requirements of the blockchains are fundamentally different.