Það var stigafjöldann sem ég véfengdi þegar andstæðingurinn svindlaði við leikslokin.

This is a very common Icelandic cleft sentence pattern, used for emphasis or contrast.

• Það var stigafjöldann sem ég véfengdi means something like It was the point total that I disputed.
• The speaker is highlighting stigafjöldann as the specific thing they challenged.

A less emphatic version would be:

• Ég véfengdi stigafjöldann þegar andstæðingurinn svindlaði við leikslokin.

So the Það var ... sem ... structure works very much like English It was ... that ....

No. Here það does not mean the demonstrative that.

In this pattern, það is an expletive/dummy subject, like English it in:

• It was the score that I disputed.

So in Það var stigafjöldann sem ég véfengdi, the word það is mainly there because Icelandic, like English, often uses this kind of formal subject in cleft sentences.

Here sem introduces the relative clause that explains the focused element:

• stigafjöldann sem ég véfengdi
• literally: the point total that I disputed

A useful thing for learners: sem does not change form for gender, number, or case. English learners often expect something like who/which/that, but Icelandic usually just uses sem.

So in this sentence:

• Það var stigafjöldann sem ég véfengdi
• It was the point total that I disputed

Because stigafjöldann is in the accusative singular definite form.

The dictionary form is:

• stigafjöldi = point total / number of points

But in the sentence, it is the direct object of véfengdi (disputed/challenged), so it has to be in the accusative:

• Ég véfengdi stigafjöldann.
• I disputed the point total.

Even though it appears near the front in the cleft sentence, it still keeps the case required by its role in the clause after sem.

A useful way to see it:

• basic sentence: Ég véfengdi stigafjöldann
• clefted version: Það var stigafjöldann sem ég véfengdi

The base form is stigafjöldi.

Here is the important idea:

• stigafjöldi = indefinite nominative singular
• stigafjöldann = definite accusative singular

So the ending changes because:

1. the noun is definite (the point total, not just a point total), and
2. it is in the accusative because it is the object of the verb.

Because both are subordinate clauses.

In Icelandic, main clauses often follow V2 word order, but subordinate clauses introduced by words like sem and þegar usually have more straightforward subject + verb order.

So:

• sem ég véfengdi = that I disputed
• þegar andstæðingurinn svindlaði = when the opponent cheated

This is why you see:

• ég véfengdi
• andstæðingurinn svindlaði

rather than a verb-first order.

Véfengdi is the past tense of véfengja.

• véfengja = to dispute, question, challenge, cast doubt on
• véfengdi = disputed, questioned, challenged

In this sentence it is:

• 1st person singular past
• because the subject is ég = I

So:

• ég véfengdi = I disputed / I challenged

Because that ending is the suffixed definite article.

The base noun is:

• andstæðingur = opponent

With the definite article:

• andstæðingurinn = the opponent

Icelandic usually attaches the to the end of the noun instead of using a separate word like English does.

In this sentence, andstæðingurinn is also the subject of svindlaði, so it is in the nominative:

• andstæðingurinn svindlaði = the opponent cheated

Við leikslokin means at the end of the game or in the closing moments of the game.

A few things are going on here:

• við can have several meanings, and in time expressions it can mean something like at / around / toward
• leikslok means end of a game/match
• this noun is very often used in the plural in Icelandic

So:

• leikslok = game end / final moments
• leikslokin = the end of the game, in a definite plural form

This kind of plural where English might use a singular is something learners just have to get used to.

Grammatically, it most naturally gives the time frame for the main event:

• It was the point total that I disputed when the opponent cheated at the end of the game.

So the idea is that the disputing happened in that situation/time context.

At the same time, because the clause itself contains svindlaði við leikslokin (cheated at the end of the game), it also naturally tells you when the cheating occurred. In normal reading, the whole phrase sets the scene: the opponent cheated at game end, and that is when the speaker disputed the point total.

Yes. A very natural non-cleft version would be:

• Ég véfengdi stigafjöldann þegar andstæðingurinn svindlaði við leikslokin.

This version is more neutral. It simply states what happened.

The original sentence:

• Það var stigafjöldann sem ég véfengdi þegar andstæðingurinn svindlaði við leikslokin.

adds emphasis, roughly like:

• It was the point total that I disputed...

So the difference is mostly one of focus and emphasis, not basic meaning.