طعام القطط في وعاء الطعام.

Yes. In Modern Standard Arabic, the verb to be is usually not stated in the present tense.

So:

• طعام القطط = the topic / subject
• في وعاء الطعام = the predicate, meaning in the food bowl

So the whole sentence means The cat food is in the food bowl even though Arabic does not use a separate present-tense is here.

If you wanted the past tense, Arabic would normally use كان:

• كان طعام القطط في وعاء الطعام = The cat food was in the food bowl

Both are examples of the iḍāfa construction, often called the genitive construct or annexation.

It works like this:

• طعام القطط = food of the cats / cat food
• وعاء الطعام = bowl of the food / more naturally food bowl

In an iḍāfa:

1. The first noun is the thing possessed or described.
2. The second noun tells whose it is, or what kind it is.

So:

• طعام = food
• القطط = the cats
  → طعام القطط = the cats’ food / cat food

And:

• وعاء = container, bowl
• الطعام = the food
  → وعاء الطعام = food bowl

Arabic often uses iḍāfa where English uses either of or a noun-noun compound.

Because in an iḍāfa construction, the first noun normally cannot take الـ.

So Arabic says:

• طعام القطط

not:

• الطعام القطط ❌

This is a rule of the construction. The first noun also normally does not take tanwīn in iḍāfa.

Even without الـ on طعام, the whole phrase can still be definite because the second noun is definite.

That is a very natural question. English often uses a singular noun as a modifier:

• cat food
• dog food
• car door

Arabic does not usually build this kind of phrase the same way. Instead, it often uses:

• an iḍāfa
• or a phrase with لِـ meaning for

So طعام القطط literally looks like food of the cats, but in natural English it can simply mean cat food.

The plural القطط is normal here because the meaning is food for cats as a kind/species, not necessarily food belonging to several specific pets.

Another common way to say it is:

• طعامٌ للقطط = food for cats

Because Arabic often uses the definite article الـ for a whole class or species.

So القطط can mean:

• the cats in a specific context
• or cats as a general category

This is different from English, where the cats usually sounds specific.

Also, in iḍāfa, if the second noun is definite, the whole phrase becomes definite:

• طعام القطط = a definite phrase

So depending on context, this may be understood as:

• the cats’ food
• or cat food

في means in.

It is a preposition, and in Arabic, prepositions make the following noun genitive.

So in:

• في وعاء الطعام

the word وعاء is in the genitive case because it follows في.

Then الطعام is also genitive, because it is the second noun in an iḍāfa:

• وعاءِ الطعامِ

So grammatically:

• في → forces وعاء into the genitive
• وعاء
  • الطعام → iḍāfa, so الطعام is genitive too

A careful fully vocalized pronunciation is:

طَعَامُ الْقِطَطِ فِي وِعَاءِ الطَّعَامِ

Approximate pronunciation:

ṭaʿāmu l-qiṭaṭi fī wiʿāʾi ṭ-ṭaʿāmi

Two useful pronunciation points:

• القطط: the ل is pronounced, because ق is a moon letter
  → al-qiṭaṭ

• الطعام: the ل is not pronounced separately, because ط is a sun letter
  → aṭ-ṭaʿām

So the article الـ is written the same way in both words, but pronounced differently.

With full vowel marks and case endings, the sentence is:

طَعَامُ الْقِطَطِ فِي وِعَاءِ الطَّعَامِ

Here is why each ending appears:

• طعامُ
  nominative, because it is the topic/subject of the nominal sentence

• القططِ
  genitive, because it is the second noun in the iḍāfa طعام القطط

• وعاءِ
  genitive, because it comes after the preposition في

• الطعامِ
  genitive, because it is the second noun in the iḍāfa وعاء الطعام

In normal unvowelled writing, these endings are not shown, and in everyday pronunciation many final short vowels are not fully pronounced.

Literally, yes, that is close to the word-for-word structure. But it sounds unnatural in English.

A more natural English translation is:

• The cat food is in the food bowl.

This is a good example of how Arabic often uses iḍāfa where English prefers:

• a noun modifier: cat food
• or a compound noun: food bowl

So literal structure and natural translation are not always the same.