Technically, yes. "Fast" is an adjective, so it should describe a noun. In this sentence, it describes a verb. In its place should be an adverb such as "quickly."
However, people frequently ignore this rule and say stuff like "we play fast" anyway.
So, technically it is wrong but, realistically, it's used that way.
A lot of games involve an element of speed. And even if they don't, they can be played at various rates.
The card games Nertz and Speed, for example, are played quickly.
Chess can be fast or slow depending on how long each player takes to plan their turn.
And, I don't know if ludas applies to musical instruments or not, but if it does, you can definitely play music at different paces.
I heard ludas arapide. Then I listened again...
The R in rapide is trilled. Since English speakers aren't accustomed to hearing trilled Rs, a full trill sound can sound like there's an additional letter somewhere around it. This effect is often amplified if it's adjacent to a consonant (the s from ludas, in this case).
The speaker vocalized his breath as he prepared to pronounce that deliciously rolled R in "rapide". I too had trouble and clicked replay about 30 times to make sure that he wasn't saying "ludasa rapide" or "ludas arapide". So, it wasn't you. There was definitely an "a" sound enunciated between "ludas" and "rapide". But, I think it was worth it to hear that fantastic rolled R.
You are right. Even in languages with plural verbs (Czech, French, Italian, Spanish…) adverbs do not depend on the number; they certainly do not in Esperanto.
However, since English (to my knowledge) has no words ending in an “-e” sound, some English-speaking beginners tend to append a short “j” to such words in Esperanto, pronouncing “ne” as “nej” (nay) and “bone” as “boŭnej” (bownay). That goes away over time.
I do not think so. (But I am not an expert...) Because adverbs depend on their verbs, but adjectives depend on their nouns. Since adjectives describes the causer of the action, it has to be shaped equally to that causer. On the other hand, the adverb is the answer to "How has been the action done?", with no connection to its causer, there is no reason to shape it like it. (Prove me wrong, please.)