I think you're wrong in your thinking and in your game playing. Yes, faking being poor to see if someone will buy you something to prove love is game playing. Game playing is childish and immature, and a bad way to handle relationships.
Buying items for someone whether that person can afford them or not does not show love. It just shows they have money and can spend it.
The fact he is dating you, the fact he is considering marriage, the fact that he will help out with rides, proves he is interested in you. The fact he spends time with you and your child that is not his, proves he is interested in you. Not whether or not he buys you flowers or shoes.
If you think game playing is a good alternative to direct communication, and buying items is proof of love, you will be in for a long road of disappointment and problem relationships.
Instead of playing immature, childish relationship games, learn how to directly communicate with your partner like an adult.
Instead of thinking buying gifts indicates love, look at their actions and how they treat you to indicate love. Any man can buy you things, few men are willing to be in a relationship with a single mom who plays relationship games. Actions and how they treat you speaks louder than a pair of shoes bought for you because you LIED.
Instead of LYING about your finances, you need to learn how to have honest discussions about them before you even really consider marriage.
When you start having honest discussions with your partner, treating your relationship like a mature adult, and stop equating gifts with love, you will also be teaching your child how to be a mature adult capable of adult relationships, instead of teaching your child to be a lying, manipulative, childish game player seeking material items in place of real caring or love.