For streaming online games at 2560 x 1440 60fps on youtube will gigabit be enough or will I have to go for 2.5 gigabit to avoid lag?
Given that the vast majority of home or even small office WAN connections are way slower than 1 gigabit, I don't think you need 2.5 Gbe. Video streaming depends on fairly intense compression to reduce the bandwidth demands.
Where you will see 2.5, 5, or 10 Gbe connections today are mostly local connections, e.g. computer to local network storage (NAS), intra-cluster comms, that sort of thing.
Unless you plan to buy a $1000+/mo commercial fiber internet plan that delivers 2+G of upstream/downstream to your location, then having 2.5G local networking will have no impact.
"A small price to pay for low ping"
What exactly do you mean? As in a 1GB/s or 2.5GB/s upload speed? If so you are sure you aren't thinking of something else.
If your network speed is faster than your Internet upload speed (which simple gigabit networks are in 99.999% home users) then you will be fine with your own network speed.
I have an 150MBit connection and I can upload 1080p real time. You dont need even close to 2.5gbit.
But if you are a pro streamer making big bucks streaming your gaming sessions and making 1grand+ a day. Maybe just get it for fun and run your own gaming servers too.