Infinitives in English typically begin with "to" (although there are exceptions), whereas infinitives in German are marked by the -en ending (although of course here there are also exceptions).
With the word play, in English one could say "I would like to play" using the infinitive "to play"
In German the sentence would be "Ich würde gerne spielen". This is also using the infinitive, although the infinitive looks different in German. Saying "Ich würde gerne zu spielen" wouldn't follow the German structure of infinitives and therefore wouldn't make sense.
In short, the structure of infinitives simply varies amongst languages. I hope this helps!