Agree with u/en43rs 's answer, so I'll just add some follow on thoughts in line with that

First thought, if you start your question with "Besides the Romans" I'd feel like every logical reason that makes you want to exclude the Romans as a too obvious answer, excludes the Greeks for the same reasons.

Then, as previously noted, you really can't begin to scope this question until you narrow it down to what type of impact you're looking for.

Let's start with Language for a moment though.

Beyond the root influence of languages (Greek, Roman, German, Chinese, etc) lets take a look at modern spread of languages as we know them today.

How many nations speak English? Spanish? Arabic?

The point of that question is not to say "oh look how great an impact those countries had on the languages we speak today". The point of that question is to hint at... hmm... WHY do the countries that speak their languages speak them? How did that happen? I.e., how many nations fell under those empires control, to the point of still having assimilated to their culture even today.

Spain recalibrated the entire future of the majority of the Americas, and the number of Spanish speaking countries in the West is pretty much a road map of that.

And HOW great was the impact of the Spanish Golden age and the territory they took over?

Well, there is a pretty fair argument that for all the attention American and French colonial slavery gets, the reality is the Spanish were major drivers in the Trans Atlantic slave trade.

Also, what about the physical, ethnic, genetic impact?

What do the Spanish and the Mongols for example, have in common?

The fact (at least I would argue) that the entire ethnic/cultural/genetic make up of entire regions was drastically, and irreversibly changed by the massive part of the native populations they either displaced or exterminate though conquest.

Put simply, there are ethno-cultural groups that used to live in regions, but don't, and maybe no longer exist at all, because the Mongols, Conquistadors, etc outright killed them. (Killed as in on the spot killed, or killed as in rounded up and sent to the silver mines until they were used up, etc etc)

Impact on World History is not a good qualifier, it's too vague. So if you want a more precise answer you need a more precise question. What kind of impact? Culturally? Linguistically? Politically? And by world history do you mean still visible today?

Because a lot of states had impact on history, like a lot. China basically defined east Asian culture, the Mongol empire is responsible for a lot of Russian history, eastern Europe was hugely impacted by Germany, Austria and Russia. France had as much an impact as the British in the make up of Africa. So on, so on.