That would be because games and apps really don't run from cards, unless you are using Marshmallow (or you have rooted your phone).
If you were running Marshmallow on the old phone, and the new one, the reason it might not read it is that if you had made the card "Internal" rather than "External", which can only be done in that OS, then it will have encrypted the card, making it only usable correctly and fully on that particular phone.
If these are apps and games you have purchased, you should be able to re-download them to the new phone.