Can connect anything with MIDI to a "game". Seek out DTXmania for a game example (not specific to the DTX)
If you want to actually learn, look at https://www.roland.com/uk/products/dt-1/ (again, can be made to work with most things)
And the eternal "what kit"? Question.... well here's my...
You have Yamaha hat controller already ? (which one - bit confusing above, you say "sticks with a Yamaha pedal" ;) ?)
- you can get a Yamaha module for not a lot on eBay if you're being "cost conscious" :) (dunno your budget or location)
Anything from anyone. All just £0.50 piezos in a shell. (pretty much anything will "handle" a double kick)
Or - as it's an ekit - it just as simple and can be more flexible and cheaper to get another pad and another single pedal.
"Alesis or Roland"
Those are two of the possible options. There are many, many more. Yamaha, ATV, 2Box, Pearl etc.
You haven't given use much to go on (bit like asking "Toyota or Ford: I need one for driving")
....so here's the "what kit" post:
What have you...
Get maple sticks.
If you're using hickory or even oak they don't flex as well, so transmit vibes.
Flex: maple > hickory > oak
And use as thin as is comfy for your finger length / hand size.
You don't need specialist expensive sticks. Cheap maples are fine. (I get brick of pairs for £20...
TD17 -->MIDI--> Strike?
Strike has MIDI in, so yes.
"Will it work with drum software"?
Assume you mean a software instrument, if so, then no reason why not as long as the Strike's MIDI THRU is on.
TD17--> MIDI --> Strike --> MIDI --> PC --> Software
Which $ ? US / CAD / AUD etc
What have you played (apart from the Alesis?)
What "samples" do you want to load? Cowbell? Three minute backing loop?
Nope. Indeed many don't come with a single bass pedal.
- it's an ekit - use two single pedals and two pads if you like. More flexible.
Don't know you intended use (bedroom, live, rehearsal...) Closed - if you don't want external souncs.
Anyway - headphones - you'll get as many responses as drummers.
SO.... Here's 700+ views on the matter to save retyping (don't know your budget or use :) ) Grab a cuppa and enjoy...
"Are Alesis cymbals interchangeable with other Alesis kits?"
Yes - but depends on the module, input and cymbal as to what features you'll get (multiple zones, choke etc)
ask over here for specifics: www.alesisdrummer.com
Many, many options to do what you want
Q; How many sounds do you need to have available in any song (= number of pads)
Q: do you want the ability to load up your own percussion sounds?
Q: What the budget - as a number - and your country/location?
Pads start from < £$€100 and go right up from...