Hello Shamal
The table that you shared comes from the Classful vs Classless routing protocols lesson. This table indicates what kind of routing these protocols support. RIPv1 supports only classful routing. That means that you cannot specify a subnet mask when indicating the networks that are advertised. The subnet mask for each class (A, B, and C) will automatically be used.
The routing protocols that support classless routing are those indicated, including EIGRP. This simply means that these protocols support the use of a subnet mask or wildcard mask to more granularly define the address space of each advertised network. This however does not mean that these protocols cannot be configured to behave in a classless manner.
In this lesson, Rene states that the auto-summary feature, when enabled, will cause the EIGRP protocol to behave in a classful manner. Configuring no auto-summary will ensure that EIGRP acts in a classless manner.
What is the default behavior? Well, according to the following Cisco documentation, auto-summary was enabled by default in older IOS versions (i.e. EIGRP behaved in a classful manner), but in newer versions, the default is that auto-summary is disabled (EIGRP behaves in a classless manner).
https://www.cisco.com/c/en/us/td/docs/ios/iproute_eigrp/command/reference/ire_book/ire_a1.html#wp1062919
In any case, because EIGRP has the capability of behaving “classlessly”, it is thus considered a classless routing protocol. Does that make sense?
I hope this has been helpful!
Laz