Clarification is needed. Your composer tells you to license your game, and you didn't do that with your previous one.
That means that you made a game and...
- didn't show it to anyone? That is, you did not publish/distribute it?
- gave it away for free, and didn't make mention of a license?
- sold it, but didn't specify a license?
- something different?
Or, the composer wants you to buy a license for the music he made for you?
These are all very different things. Some are more harmless, some are mostly harmless, and some are outright troublesome.
For example, simply not distributing your game is harmless, it's just a shame you made it and nobody gets to see it.
Distributing a game for free without a license is "mostly" harmless. For the most part, no evil things will happen except you don't get any money (which you didn't ask for anyway) and people can do just what they want with your software (they can, and will, do what they want anyway, so who cares!). Be however aware that it is still possible to ask for damages (for moronic reasons such as fitness for an implied use, and for other more valid reasons) in some countries with cowboy laws, even if you gave it away for free. Which means in the most extreme, most perverse possible case, someone might infringe you for causing that meltdown in the city's nuclear powerplant because everybody was busy playing your pong game instead of responding to blinking red lights. Or a car driver might blame an accident on you because he was too busy looking at his phone with your game on it.
Now, selling a game without a license (or rather, selling the game) is another thing. This is very bad. You do not normally sell software, never, not ever (well, except when a big $$$ company buys it from you). Instead, you sell a license, which is a limited (usually non-exclusive) right to use that software. Use, not own.
This is usually explicitly stated in the lengthy lawyerese of the license agreement, and often part of the "by doing XYZ you agree..." clause on the sticker on the shrinkwrap (or above the download link), too.
If you don't do that, someone might argue that they bought the software (that is, all rights to it) instead. Which, although every sane person would agree that this is nonsensical, is technically true. Now, in states with cowboy laws, this would allow someone to successfully draw you to court (and win the lawsuit) because you later sold the game (which you no longer owned) to someone else.