Övervakningskamerans inspelning visar stölden.

Because Swedish makes compounds very freely.

Here, the basic compound is:

• övervakning = surveillance / monitoring
• kamera = camera
• övervakningskamera = surveillance camera

Then more endings are added:

• övervakningskameran = the surveillance camera
• övervakningskamerans = the surveillance camera’s

So the whole first word is built step by step rather than written as separate words.

They show definiteness and possession.

• övervakningskamera = a surveillance camera
• övervakningskameran = the surveillance camera
• övervakningskamerans = the surveillance camera’s

So:

• -an = the definite ending for this en-word
• -s = the genitive ending, like English ’s

That means övervakningskamerans inspelning literally means the surveillance camera’s recording.

Because after a possessive/genitive expression, Swedish normally uses the possessed noun in its indefinite form.

So Swedish says:

• övervakningskamerans inspelning

not:

• övervakningskamerans inspelningen

Even though inspelning is indefinite in form, the whole phrase is still understood as definite: the surveillance camera’s recording.

This is very common in Swedish:

• mannens bil = the man’s car
• lärarens bok = the teacher’s book
• övervakningskamerans inspelning = the surveillance camera’s recording

Because it refers to a specific theft.

• stöld = theft / a theft
• stölden = the theft

In this sentence, the recording shows a particular theft, so Swedish uses the definite form stölden.

It is a normal Swedish subject–verb–object sentence:

• Övervakningskamerans inspelning = subject
• visar = verb
• stölden = object

So literally:

• The surveillance camera’s recording / The recording from the surveillance camera
• shows
• the theft

This is very standard word order for a main clause in Swedish.

Because Swedish verbs do not change for person the way English verbs do.

In English:

• I show
• you show
• he/she shows

In Swedish, the present tense stays the same:

• jag visar
• du visar
• den visar

So visar is simply the present tense of visa = to show.

No. Swedish does not add an extra article here.

The definiteness is already expressed by the genitive phrase:

• övervakningskamerans inspelning

That whole phrase already means something definite: the surveillance camera’s recording.

So Swedish does not say something like:

• den övervakningskamerans inspelning

in this context.

Yes. A very natural alternative is:

• Inspelningen från övervakningskameran visar stölden.

That means:

• The recording from the surveillance camera shows the theft.

The difference is mostly in structure:

• övervakningskamerans inspelning = the surveillance camera’s recording
• inspelningen från övervakningskameran = the recording from the surveillance camera

Both are good Swedish. The original sentence is a bit more compact.

Like this:

• övervakning = surveillance / monitoring
• övervakningskamera = surveillance camera
• övervakningskamerans = the surveillance camera’s
• inspelning = recording
• visar = shows
• stölden = the theft

So the full sentence is literally:

• The surveillance camera’s recording shows the theft.