After recently reading this, I wonder if the games I downloaded and currently own on Steam can be passed on to my son. Will Steam allow transfer of ownership of my account? If it is written in my last will and testament, will they accept it?
Well, it's a bit more clear cut for games than music.
Games are software, software is always required to have valid license to be used. Using software in a breach of license is piracy. Steam EULA makes it very clear that you don't own the games:
Valve hereby grants, and you accept, a limited, terminable, non-exclusive license and right to use the Software for your personal use in accordance with this Agreement, including the Subscription Terms. The Software is licensed, not sold. Your license confers no title or ownership in the Software.
Also according to EULA games nor account cannot be transferred to another person:
You are entitled to use the Software for your own personal use, but you are not entitled to: (i) sell, grant a security interest in or transfer reproductions of the Software to other parties in any way, nor to rent, lease or license the Software to others without the prior written consent of Valve, except to the extent expressly permitted elsewhere in this Agreement (including any Subscription Terms or Rules of Use);
There comes interesting part. If you're living outside of European Union, the choice of law is WA, USA. So you're out of luck. However if you live in European Union, there is interesting part about choice of law:
For EU Subscribers:
You agree that this Agreement shall be deemed to have been made and executed in the Grand Duchy of Luxembourg and that it is subject to the laws of Luxembourg, excluding the law of conflicts and the Convention on Contracts for the International Sale of Goods (CISG). However, where the laws of Luxembourg provide a lower degree of consumer protection than the laws of your country of residence, the consumer protection laws of your country shall prevail. In any dispute arising under this Agreement, the prevailing party will be entitled to attorneys' fees and expenses.
Why is it interesting? There have been some countries, where it has been ruled that preventing re-sale or transfer of software licenses is violation of free market, thus the "non-transferable" clauses are invalid. And there have been rulings confirming it on EU level.