Using a power strip in an old home that was build back in 1955

My first question would be what are you planning to plug into this box?  With so many plugs, will you be overloading the circuit?  Do you have the opportunity to run a dedicated gounded line fron your main panel?  If grounding is important,  I don't see that plugging things into a power strip that goes into a non grounded outlet will achieve anything?

My old house was built in 1953. Same type of outlet wiring. A circuit breaker panel instead of fuses. I never had a problem no matter how many components I plugged into the outlets. So why worry? Use whatever power strip you want. They won't affect the sound of your gear. 

You will need an adapter plug to use that Amazon strip with your two-prong AC outlets.

To provide some additional information.

I've been using power strips for years. Most of the outlets in my home are the 3 prong type, but are not grounded. My room has a 2 prong ungrounded outlet. I added a 2 to 3 prong adapter and added a power strip. No issues.

In the living room, where my tv is, the outlet is a 3 prong ungrounded outlet. I plan to upgrade my power strip from a 12 to a 22 or 24 outlet power strip. I'd plug in gaming consoles along with upscalers.

What I don't want to have happen is to plug in a 22 outlet power strip and have a wiring fault occur so that the power strip doesn't function. Although it doesn't seem like a problem would occur.

I'm not an electrician, but this sounds like living dangerously to me. I think that it's illegal in my jurisdiction to have a three-hole receptacle which isn't grounded. In any case, I would never do it because that ground pin can save your life.

Also, most surge suppressors route excess energy into that ground pin. IF that's connected to nothing, then protection is nil. The first thing I did when I moved into a 1950's house was upgrade all the important circuits to 3-conductor, along with a 200A service.

Just my $.02 - but I strongly urge you to consult an electrician.