How should we interpret this quote from Pope Pius XI?

In the comments there is some discussion about context. Until that is answered, I am afraid a more general answer will have to do for the moment. But maybe it helps you on your way:

Has the Church provided a way for us to interpret such a statement?

In general it is useful to understand the position of the pope and of anything he says. The dogma on infallibility may sound as if anything a pope says is to be believed as religious truth, but that is not the case. There are certain contextual aspects on any dogmatic statement of a pope. What a pope says is NOT to be understood as infallible unless, popular said, it is very clear that it is. Such statements are extremely rare.

But that doesn’t imply that what a pope says has the same weight as what any person in the world may say. The pope is elected to sit on the chair of the apostle Peter, to be the rock of unity of the Church of Christ (well, that is what we believe, non-Catholic Christians may believe otherwise of course) and we do believe the Holy Spirit, the 3rd Person of God, leads the Church, so the position of the pope is very important indeed. What a pope says is not to be taken lightly, even if it doesn’t have a formal, dogmatic status.

But that still doesn’t tell you how to interpret his words. As in all things, the words of a pope should be listened to with faith, with guidance by the Church. It is very good indeed to consider by yourself what words mean, from Holy Scripture, from a pope, from a sermon in your local parish. But always challenge your personal views by the views of the Church. So if you ask “what did pope Pius XI mean exactly by these words?” you should try to understand the viewpoints, the teachings of this pope more general, and even more try to understand the teachings of the Church about this particular subject.

It is rather seldom that you can take one sentence from Holy Scripture, from a pope, or any other Catholic source, and answer the meaning of it by one other simple statement.

Are you not a very spiritual person if you don’t pray the rosary?

I can’t possibly know for certain what pope Pius XI exactly thought in private, but it isn’t Church teaching that praying the rosary is a litmus test for your level of spirituality. I would even say on the contrary. The spiritual treasury of the Church is very well filled with different gifts to mankind. The rosary is a very deep and valuable prayer for any spiritual life, but it isn’t the only one. Another one, just as an example, is the liturgy of the hours, the daily prayer cycle around the book of psalms, all clergy and religious orders pray.

And please note there is no contest to be the most spiritual person, more than your brother or sister. Living a spiritual life is something you, and everybody, is invited to. What is good for one person may not be the best for another.

Is there room for the not so absolute?

You refer to the teachings about baptism, in a way I interpret as a question if statements of the Church are to be understood as absolute. Do you need to be baptised? Yes. Can you enter heaven without being baptised? Yes.

The thing is, the Church does teach some things as really, really absolute. But a lot of things are more of the form “we know for certain this, but it is always God's freedom to let His love be greater than this”. Your baptism question is a great example. Yes, being baptised does, absolutely certainly, make us die in our old life and be reborn, resurrected, in Christ. We don’t just hope so, we know so. And this gives us an open invitation to enter heaven when we leave this earth. But can you reason from this starting point to a negative? Can you say: therefore, if you didn’t receive baptism, heaven is closed for you? No, you cannot. It is always God’s love that can still allow you into heaven.

For the rosary, you can follow the same path of thinking: yes, the rosary is a very good prayer. But if you don’t pray the rosary, that doesn’t make you bad.