By P2PK transactions you mean the input AND the ouput? They both (or more) must be p2pk addresses in order to not show it? Because I can see that two out of the three transactions above are normally shown on electrum and since the address is P2PKH, all of its outputs are P2PK. You probably mean something different, that I'll kindly ask you to explain it more.
Public keys are not technically addresses as addresses are the hash of the public key.
Let's establish some things first for clarity. 1M311YjWBuHbZhLDynBKFCTXosJe7d2Boi did not exist in 2009; Satoshi (or whichever miner who mined that block) did not send the Bitcoins to a Bitcoin address but to a public key. Blockexplorers tend to oversimplify this and associate public keys with the corresponding addresses had it been expressed as an address. You can check it yourself by decoding the raw transaction and see that it is infact a P2PK transaction.
Blockexplorers will associate P2PK transactions to the corresponding addresses and that is fine. But, in the case of Electrum, your query to the server would be your watch-only
address which is not a public key. Since Electrum nodes only fetch the transactions related to that script hash (ie. the two transactions shown) as they do not do what blockexplorers usually do, you would only see the transactions that are sent to and from that address, not public key.
Are both of the following transactions P2PK?
1) P2PKH Address A ---> 1 BTC ---> P2PKH Address B.
2) Non-P2PKH Address A ---> 1 BTC ---> P2PKH Address B.
No. P2PK is Pay-to-Public-Key which means you're not specifying the outputs as an address but rather an ECDSA public key.