Yes. In Buddha Dhamma, there is no need to do “conventional kasina meditation” in the sense of yogis who keep looking at a fire, chant “fire, fire, ..” and be absorbed in that arammana.
– Some automatically end up with abhinna powers with the Arahanthood. Of course, that does not happen often. The case of Minister Santati is an exceptional case.
Let us summarize the account on Santati’ per the link you provided. Others may want to read the account in the link provided above.
1. He was a Minister to King Pasenadi and won a battle for the King. After celebrating the victory for seven days, Santati was drunk when the Buddha saw him earlier in the day. Later in the day, one of the dancing girls who entertained him died of exhaustion, and Minister Santati was thoroughly distressed. He went to see the Buddha and the Buddha explained to him in a single verse why he became so distressed. The translation there is not that good, but you can get the idea.
“The root cause for ANY kind of suffering is attachment to worldly things (upādāna.)”
– I have discussed this in detail recently: “Concepts of Upādāna and Upādānakkhandha”
2. Just by hearing that verse, minister Santati attained Arahanthood. Not only that, he had attained abhinna powers as well. That is the key point to think about. This account is very similar to that of Vne. Culapanthaka, who had been unable to even memorize a single verse for many months, but attained Arahanthood complete with abhinna powers in a day!
– Also see the amazing account of Ven. Cūḷapanthaka in #2 of “Are There Procedures for Attaining Magga Phala, Jhāna and Abhiññā?”
3. With his abhinna powers, Minister Santati saw that his life is coming to an end. With Buddha’s consent, he rose to the sky and set himself on fire at the moment of death. In the version that I had heard, the Buddha actually asked him to do that so that others could see that he had attained Arahanthood complete with abhinna powers.
4. The point here is that Minister Santati had not cultivated any jhana. He was a warrior who had just led an army to battle. But apparently, he had fulfilled most of the paramita in his prior lives, and “needed only a little push” to get to the Arahanthood.
– He had cultivated jhana in prior lives as well and that is why he (and Ven. Culapanthaka) automatically attained abhinna powers together with the Arahanthood.