Die Punkteleiste zeigt die Siegbedingung.

They are both the definite article the, but they belong to different nouns:

• die Punkteleiste = the score bar / points bar
• die Siegbedingung = the win condition

Both nouns are feminine singular, and for feminine singular nouns, the article is die in both the nominative and the accusative.

So here:

• die Punkteleiste = nominative, the subject
• die Siegbedingung = accusative, the direct object

In a normal German main clause, the noun phrase before the verb is usually understood as the subject, especially when both noun phrases look the same in form.

So in:

Die Punkteleiste zeigt die Siegbedingung.

the usual reading is:

• Die Punkteleiste = subject
• zeigt = verb
• die Siegbedingung = object

English does the same thing with word order:

• The score bar shows the win condition
  not
• The win condition shows the score bar

Even though the article forms do not help here, the normal word order does.

Because zeigt is the correct present-tense form for a third-person singular subject.

The infinitive is zeigen = to show.

Conjugation in the present tense:

• ich zeige
• du zeigst
• er/sie/es zeigt
• wir zeigen
• ihr zeigt
• sie/Sie zeigen

Since die Punkteleiste is singular, German uses zeigt.

Yes. German very often combines nouns into one compound word.

Punkteleiste is made from:

• Punkte = points
• Leiste = bar / strip

So Punkteleiste literally means something like points bar, and in natural English it could be score bar or points bar, depending on context.

This is very normal in German. Instead of writing several separate words, German often builds one longer noun.

In German compounds, the first part is not always the basic singular form. Very often it appears in a form that sounds more natural in compounds, and sometimes that form looks like a plural.

Here:

• Punkt = point
• Punkte = points

Punkteleiste suggests a bar connected with points in general, not just one single point.

This kind of pattern is common in German compounds, but it is not always fully predictable, so learners often just have to get used to common compound forms.

The gender of a German compound noun is determined by the last part.

Here, the last part is Leiste:

• die Leiste = the bar / strip

Because Leiste is feminine, the whole compound is feminine:

• die Punkteleiste

This is a very useful rule for compound nouns in German.

It is another compound noun:

• Sieg = victory / win
• Bedingung = condition / requirement

So Siegbedingung means victory condition, win condition, or condition for victory, depending on context.

Again, the last part determines the gender:

• die Bedingung is feminine
  so
• die Siegbedingung is also feminine

No. zeigen can mean several related things, such as:

• show
• display
• indicate

So depending on context, this sentence could sound natural in English as:

• The score bar shows the win condition.
• The score bar displays the win condition.
• The score bar indicates the win condition.

If this is a user interface or game context, display or show may both work well.

Because in German, all nouns are capitalized.

So in this sentence:

• Punkteleiste is a noun
• Siegbedingung is a noun

That is why they begin with capital letters.

Also, Die is capitalized here because it is the first word of the sentence, not because articles are normally capitalized.

Yes, but in a normal statement the finite verb usually stays in second position.

The standard order here is:

• Die Punkteleiste (topic/subject)
• zeigt (verb)
• die Siegbedingung (object)

You can move other elements to the front in German, but then the verb still stays second. With this particular sentence, switching the two noun phrases could create confusion, because both start with die and both are feminine singular.

So for clarity, Die Punkteleiste zeigt die Siegbedingung is the most straightforward version.