Learn Arabic (Modern Standard): اللاعب الحادي عشر في الفريق ممتاز. - The eleventh player on the team is excellent.

This is exactly what it means to be مبني على فتح الجزأين (indeclinable with a Fatha on both parts). Compound ordinal numbers from 11th to 19th are locked in this state. Even though the number acts as an adjective describing the subject اللاعب (which is nominative and ends in a Damma), the compound number ignores the grammatical case and keeps its fixed form.

Why is the word for 'first' here الحادي instead of الأول?

When 'first' is part of a compound number (like 11th) or combined with tens (like 21st, 31st), Arabic uses the special form الحادي for masculine and الحادية for feminine. You only use الأول when saying 'the first' entirely on its own.

Why does only the first half of الحادي عشر get the definite article الـ?

That is the standard rule for making compound ordinal numbers (11th-19th) definite. You only attach the definite article الـ to the first word (the unit digit). The second word, عشر, never takes الـ in these compounds.

How do we know the sentence means 'The eleventh player is excellent' and not 'The excellent eleventh player'?