Note the "or's". Not all prayer is worship. A request for help is not worship. The Mass is a prayer of worship. A prayer like "Heavenly Father I adore Thee..." is worship. A prayer like "Heavenly Father I ask that the Indians beat the Yankees" is not worship it is intercessory prayer.
Let’s try re-parsing those “or’s”
Prayer is a request for help OR expression of thanks to God (or an object of worship that is not God).
Therefore, prayer is addressed to an object of worship — requesting help, or thanking God is still worshipping God. Or, it is worshipping someone/something else other than God.
A request for help is not necessarily a prayer — i.e., “Mom! Please help me!” But, if you pray to your Mother and ask for prayer, what are you doing? Just asking for help? NO! You are worshipping her; you have elevated her from a simple individual who can be asked to one who must be approached by prayer. Doesn’t that imply a certain elevation from the natural to the supernatural? If you “ask” God for help, whether it’s under your breath, or a silent request, you are praying, are you not? Or, can you go up to him and say, “hey, I want the Indians to beat the Yankees.” The content is not the issue - it’s the mode. Praying is worshipping. Prayer is the entering into the presence of God — our object of worship. Unless Mary or the Saints are being prayed to, then THEY are the object... and idolatry ensues.
The Lord’s Prayer is a model prayer. When the disciples asked Christ to teach them to pray, Christ said, “pray then like this:” In this model, Christ teaches the disciples to (according to your example) WORSHIP God by asking his name to be hallowed, for his will to be done.... So, every prayer is to be worshipful, no?
And, finally, I will be praying to God (no one else!) for those who feel that anyone besides The Lord deserves worship.
Hoss