As the PC is not sending any IGMP joins you can't really benefit from IGMP snooping.
IGMP snooping relies on listening to (snooping) passing IGMP packets. These packets contain information on which multicast groups the PC wants to join. The switch is then able to make a decision on which ports to send multicast traffic for the group to and which ones to block.
Now consider a group where IGMP is not operating. The source and receivers would need to be on the same VLAN. If you enabled IGMP snooping in this case and there was no IGMP traffic to snoop, the switch will not have any ports in its IGMP snooping table for the group, so the traffic would get black holed. To avoid this, if the switch doesn't receive any IGMP packets for the group it doesn't track the group and instead floods the traffic.
So in your case the traffic is flooded as the group is not learned as there are no IGMP packets.
You could try configuring IGMP on the L3 switch for VLAN 10, although if the PC is not sending joins now, it may not send them when it gets a query.
Note: Some vendors implement a feature for source only VLANs where the group can be learned by listening to the multicast source for cases where there are no receivers on the VLAN. IGMP also adds ports where IGMP queriers can be heard to the table, so now the switch can efficiently forward traffic from the source to the router without flooding and without receiving any IGMP packets.
Here is the section in RFC 4541 that talks about this issue:
An unregistered packet is defined as an IPv4 multicast packet with a
destination address which does not match any of the groups announced
in earlier IGMP Membership Reports.
If a switch receives an unregistered packet, it must forward that
packet on all ports to which an IGMP router is attached. A switch may
default to forwarding unregistered packets on all ports. Switches that
do not forward unregistered packets to all ports must include a
configuration option to force the flooding of unregistered packets on
So if you try the advice above (configure "ip igmp" on VLAN 10 of the L3 core switch), your core will send IGMP queries and the switch can then learn the location of the IGMP router. It may then revert to sending any traffic for unregistered groups to the core only.