Learn Spanish (Latin America): Mientras más visito el retiro, más quiero aislarme. - The more I visit the retreat, the more I want to isolate myself.

In Latin America, mientras más... más... is the most common way to say "the more [X]... the more [Y]". You will also see cuanto más... más... in textbooks and it is understood everywhere (and preferred in Spain), but mientras más sounds very natural in everyday Latin American Spanish.

This lesson is about using el + infinitive. Is el retiro an example of that?

No, retiro here is just a regular noun meaning "the retreat" or "the sanctuary". To make an articulated infinitive, you must use the infinitive form of a verb. If we were using the verb retirar (to withdraw), the articulated infinitive would be el retirar or el retirarse.

Could I use an articulated infinitive like el aislarme with the verb quiero?

Not in this exact structure. We generally use el + infinitive when the action is the subject of the sentence (e.g., El aislarme me ayuda a pensar = Isolating myself helps me think). In this sentence, aislarme is the object of quiero (what you want to do), so we just use the bare infinitive.

Could I say más me quiero aislar instead of más quiero aislarme?