Why does abstract class have to implement all methods from interface?

You need to re-write all of the members/methods in the interface and add the abstract keyword to them, so in your case:

interface baseInter {
    name: string;
    test();
}

abstract class abs implements baseInter {
    abstract name: string;
    abstract test();
}

(code in playground)

There was a suggestion for it: Missing property declaration in abstract class implementing interfaces but it was declined for this reason:

Although, the convenience of not writing the declaration would be
nice, the possible confusion/complexity arising from this change would
not warrant it. by examine the declaration, it is not clear which
members appear on the type, is it all properties, methods, or
properties with call signatures; would they be considered abstract?
optional?