Unser Team punktet, doch das Pubquiz bleibt unentschieden.

Because Team is grammatically neuter in German: das Team.

The possessive determiner unser- changes its ending depending on gender, case, and number. In the nominative singular neuter, it stays unser:

• unser Team
• unser Haus

So unser Team means our team.

Because Team is treated as a singular noun in German, even though it refers to a group of people.

So German says:

• Das Team punktet. = The team scores / is scoring.

Just like in standard American English, the verb agrees with the singular noun Team, not with the individual members.

punktet comes from the verb punkten, which means to score points, to earn points, or sometimes more generally to do well / score highly.

Here it most naturally means that the team is getting points in the quiz.

Form breakdown:

• punkten = infinitive
• punktet = 3rd person singular present tense

So Unser Team punktet means Our team is scoring or Our team scores.

Here, doch is being used as a coordinating conjunction, and yes, in this sentence it means something like but, yet, or however.

So:

• Unser Team punktet, doch das Pubquiz bleibt unentschieden.

means:

• Our team is scoring, but the pub quiz remains tied.

This is different from other uses of doch, which can mean things like after all, actually, or can be used to contradict a negative statement.

Because doch here is a coordinating conjunction, like aber.

Coordinating conjunctions do not change the normal word order of the clause that follows. So you get a normal main clause:

• doch das Pubquiz bleibt unentschieden

with the verb still in the usual second-position main-clause pattern.

Compare:

• ..., doch das Pubquiz bleibt unentschieden.
• ..., aber das Pubquiz bleibt unentschieden.

Both work with normal main-clause word order.

Pubquiz is a noun, and in this sentence it is treated as neuter: das Pubquiz.

That is simply the standard gender for this word here. As with all German nouns, you usually have to learn the noun together with its article:

• das Pubquiz

Also, German nouns are always capitalized, so Pubquiz begins with a capital letter.

Here, bleibt is from bleiben, which can mean to remain or to stay.

It works like a linking verb here, connecting the subject to an adjective:

• das Pubquiz bleibt unentschieden

So:

• bleibt = remains
• unentschieden = predicate adjective

This is similar to:

• Das Spiel bleibt spannend. = The game remains exciting.
• Die Lage bleibt unklar. = The situation remains unclear.

Because it is a predicate adjective, not an adjective directly in front of a noun.

In German, adjectives usually only take endings when they come before a noun:

• ein unentschiedenes Spiel = a tied game

But after verbs like sein, bleiben, and werden, the adjective normally has no ending:

• Das Spiel ist unentschieden.
• Das Pubquiz bleibt unentschieden.

So unentschieden stays in its basic form here.

Both are possible meanings in different contexts, but here it means tied / drawn.

In contests, games, quizzes, or sports results, unentschieden usually means that neither side is ahead:

• Das Spiel endet unentschieden. = The game ends in a draw.

So in this sentence, even though the team is scoring, the overall pub quiz is still level or tied.

Yes. Aber would also be natural:

• Unser Team punktet, aber das Pubquiz bleibt unentschieden.

The difference is mostly one of style and nuance. In this sentence, doch sounds a little more literary or slightly more contrastive, while aber is the most common everyday word for but.

Both are correct.